In his book on P max [7], Woodin presents a collection of partial orders whose extensions satisfy strong club guessing principles on ω | . In this paper we employ one of the techniques from this book to produce P max variations which separate various club guessing principles. The principle (+) and its variants are weak guessing principles which were first considered by the second author [4] while studying games of length ω (...) | . It was shown in [1] that the Continuum Hypothesis does not imply (+) and that (+) does not imply the existence of a club guessing sequence on ω | . In this paper we give an alternate proof of the second of these results, using Woodin's P max technology, showing that a strengthening of (+) does not imply a weakening of club guessing known as the Interval Hitting Principle. The main technique in this paper, in addition to the standard P m a x machinery, is the use of condensation principles to build suitable iterations. (shrink)

Club guessing principles were introduced by Shelah as a weakening of Jensen’s diamond. Most spectacularly, they were used to prove Shelah’s $\textsf{ZFC}$ bound on $2^{\aleph _\omega }$. These principles have found many other applications: in cardinal arithmetic and PCF theory; in the construction of combinatorial objects on uncountable cardinals such as Jónsson algebras, strong colourings, Souslin trees, and pathological graphs; to the non-existence of universals in model theory; to the non-existence of forcing axioms at higher uncountable (...) cardinals; and many more.In this paper, the first part of a series, we survey various forms of club guessing that have appeared in the literature, and then systematically study the various ways in which a club guessing sequence can be improved, especially in the way the frequency of guessing is calibrated.We include an expository section intended for those unfamiliar with club guessing and which can be read independently of the rest of the article. (shrink)

König, Larson and Yoshinobu initiated the study of principles for guessing generalized clubs, and introduced a construction of a higher Souslin tree from the strong guessing principle.Complementary to the author’s work on the validity of diamond and non-saturation at the successor of singulars, we deal here with a successor of regulars. It is established that even the non-strong guessing principle entails non-saturation, and that, assuming the necessary cardinal arithmetic configuration, entails a diamond-type principle which suffices for (...) the construction of a higher Souslin tree.We also establish the consistency of GCH with the failure of the weakest form of generalized club guessing. This, in particular, settles a question from the original paper. (shrink)

We shall show the consistency of CH+ᄀ(+) and CH+(+)+ there are no club guessing sequences on ω₁. We shall also prove that ◊⁺ does not imply the existence of a strong club guessing sequence ω₁.

The Theme. Strong forcing axioms like Martin’s Maximum give a reasonably satisfactory structural analysis of $H(\omega _2)$. A broad program in modern Set Theory is searching for strong forcing axioms beyond $\omega _1$. In other words, one would like to figure out the structural properties of taller initial segments of the universe. However, the classical techniques of forcing iterations seem unable to bypass the obstacles, as the resulting forcings axioms beyond $\omega _1$ have not thus far been strong enough! However, (...) with his celebrated work on generalised side conditions, I. Neeman introduced us to a novel paradigm to iterate forcings. In particular, he could, among other things, reprove the consistency of the Proper Forcing Axiom using an iterated forcing with finite supports. In 2015, using his technology of virtual models, Veličković built up an iteration of semi-proper forcings with finite supports, hence reproving the consistency of Martin’s Maximum, an achievement leading to the notion of a virtual model.In this thesis, we are interested in constructing forcing notions with finitely many virtual models as side conditions to preserve three uncountable cardinals. The thesis constitutes six chapters and three appendices that amount to 118 pages, where Section 1 is devoted to preliminaries, and Section 2 is a warm-up about the scaffolding poset of a proper forcing. In Section 3, we present the general theory of virtual models in the context of forcing with sets of models of two types, where we, e.g., define the “meet” between two virtual models and prove its properties.The main results are joint with Boban Veličković, and partly appeared in Guessing models and the approachability ideal, J. Math. Log. 21 (2021).Pure Side Conditions. In Section 4, we use two types of virtual models (countable and large non-transitive ones induced by a supercompact cardinal, which we call Magidor models) to construct our forcing with pure side conditions. The forcing covertly uses a third type of models that are transitive. We also add decorations to the conditions to add many clubs in the generic $\omega _2$. In contrast to Neeman’s method, we do not have a single chain, but $\alpha $ -chains, for an ordinal $\alpha $ with $V_\alpha \prec V_\lambda $. Thus, starting from suitable large cardinals $\kappa <\lambda $, we construct a forcing notion whose conditions are finite sets of virtual models described earlier. The forcing is strongly proper, preserves $\kappa $, and has the $\lambda $ -Knaster property. The relevant quotients of the forcing are strongly proper, which helps us prove strong guessing model principles. The construction is generalisable to a ${<}\mu $ -closed forcing, for any given cardinal $\mu $ with $\mu ^{<\mu }=\mu <\kappa $.The Iteration Theorem. In Section 5, we use the forcing with pure side conditions to iterate a subclass of proper and $\aleph _2$ -c.c. forcings and obtain a forcing axiom at the level of $\aleph _2$. The iterable class is closely related to Asperó–Mota’s forcing axiom for finitely proper forcings.Guessing Model Principles. Section 6 encompasses the main parts of the thesis. We prove the consistency of the guessing principle $\mathrm {GMP}^+(\omega _3,\omega _1)$ that states for any cardinal ${\theta \geq \omega _3}$, the set of $\aleph _2$ -sized elementary submodels M of $H(\theta )$, which are the union of an $\omega _1$ -continuous $\in $ -chain of $\omega _1$ -guessing, I.C. models is stationary in $\mathcal P_{\omega _3}(H(\theta ))$. The consistency and consequences of this principle are demonstrated in the following diagram. We also prove that one can obtain the above guessing models in a way that the $\omega _1$ -sized $\omega _1$ -guessing models remain $\omega _1$ -guessing model in any outer transitive model with the same $\omega _1$, and we denote this principle by $\rm{SGMP}^+(\omega_3,\omega_1)$.In the following diagram, $\mathrm{TP}$ stands for the tree property; $w\mathrm{KH}$ stands for the weak Kurepa Hypothesis; $\mathrm{MP}$ stands for Mitchell property, i.e., the approachability ideal is trivial modulo the nonstationary ideal; $\mathrm{AP}$ stands for the approachability property; $\mathrm {AMTP}(\kappa ^+)$ states that if $2^\kappa <\aleph _{\kappa ^+}$, then every forcing which adds a new subset of $\kappa ^+$ whose initial segments are in the ground model, collapses some cardinal $\leq 2^{\kappa }$. The dotted arrow denotes the relative consistency, while others are logical implications.Appendices. Appendix A includes merely the above diagram. Appendix B presents a proof of the Mapping Reflection Principle with finite conditions under $\mathrm {PFA}$. Appendix C contains open problems. Finally, the thesis’s bibliography consists of 42 items.Abstract prepared by Rahman MohammadpourE-mail: rahmanmohammadpour@gmail.comURL: https://theses.hal.science/tel-03209264. (shrink)

We survey the use of club guessing and other PCF constructs in the context of showing that a given partially ordered class of objects does not have a largest, or a universal, element.

It is shown in this paper that it is consistent (relative to almost huge cardinals) for various club guessing ideals to be saturated.

We investigate club guessing sequences and filters. We prove that assuming V=L, there exists a strong club guessing sequence on μ if and only if μ is not ineffable for every uncountable regular cardinal μ. We also prove that for every uncountable regular cardinal μ, relative to the existence of a Woodin cardinal above μ, it is consistent that every tail club guessing ideal on μ is precipitous.

We outline the proof of the consistency that there exists a saturated tail club guessing ideal on ω₁ which is not a restriction of the nonstationary ideal. A new class of forcing notions and the forcing axiom for the class are introduced for this purpose.

Suppose that T^∗ is an ω_1-Aronszajn tree with no stationary antichain. We introduce a forcing axiom PFA(T^∗) for proper forcings which preserve these properties of T^∗. We prove that PFA(T^∗) implies many of the strong consequences of PFA, such as the failure of very weak club guessing, that all of the cardinal characteristics of the continuum are greater than ω_1, and the P-ideal dichotomy. On the other hand, PFA(T^∗) implies some of the consequences of diamond principles, such (...) as the existence of Knaster forcings which are not stationarily Knaster. (shrink)

We obtain very strong coloring theorems at successors of singular cardinals from failures of certain instances of simultaneous reflection of stationary sets. In particular, the simplest of our results establishes that if μ is singular and , then there is a regular cardinal θ<μ such that any fewer than cf stationary subsets of must reflect simultaneously.

We investigate the interaction between compactness principles and guessing principles in the Radin forcing extensions. In particular, we show that in any Radin forcing extension with respect to a measure sequence on [Formula: see text], if [Formula: see text] is weakly compact, then [Formula: see text] holds. This provides contrast with a well-known theorem of Woodin, who showed that in a certain Radin extension over a suitably prepared ground model relative to the existence of large cardinals, the (...) diamond principle fails at a strongly inaccessible Mahlo cardinal. Refining the analysis of the Radin extensions, we consistently demonstrate a scenario where a compactness principle, stronger than the diagonal stationary reflection principle, holds yet the diamond principle fails at a strongly inaccessible cardinal, improving a result from [O. B. -Neria, Diamonds, compactness, and measure sequences, J. Math. Log. 19(1) (2019) 1950002]. (shrink)

We prove that it is consistent that there exists a saturated tail club guessing ideal on ω1 which is not a restriction of the non-stationary ideal. Two proofs are presented. The first one uses a new forcing axiom whose consistency can be proved from a supercompact cardinal. The resulting model can satisfy either CH or 20=2. The second one is a direct proof from a Woodin cardinal, which gives a witnessing model with CH.

I develop a general framework with a rationality constraint that shows how coherently to represent and deal with second-order information about one's own judgmental reliability. It is a rejection of and generalization away from the typical Bayesian requirements of unconditional judgmental self-respect and perfect knowledge of one's own beliefs, and is defended by appeal to the Principal Principle. This yields consequences about maintaining unity of the self, about symmetries and asymmetries between the first- and third-person, and a principled way of (...) knowing when to stop second-guessing oneself. Peer disagreement is treated as a special case where one doubts oneself because of news that an intellectual equal disagrees. This framework, and variants of it, imply that the typically stated belief that an equally reliably peer disagrees is incoherent, and thus that pure rationality constraints without further substantive information cannot give an answer as to what to do. The framework also shows that treating both ourselves and others as thermometers in the disagreement situation does not imply the Equal Weight view. (shrink)

An ℵ1-Souslin tree is a complicated combinatorial object whose existence cannot be decided on the grounds of ZFC alone. But fifteen years after Tennenbaum and Jech independently devised notions of forcing for introducing such a tree, Shelah proved that already the simplest forcing notion—Cohen forcing—adds an ℵ1-Souslin tree. In this article, we identify a rather large class of notions of forcing that, assuming a GCH-type hypothesis, add a λ+-Souslin tree. This class includes Prikry, Magidor, and Radin forcing.

We give an affirmative answer to Brendle's and Hrušák's question of whether the club principle together with h > N₁ is consistent. We work with a class of axiom A forcings with countable conditions such that q ≥ n p is determined by finitely many elements in the conditions p and q and that all strengthenings of a condition are subsets, and replace many names by actual sets. There are two types of technique: one for tree-like forcings and one (...) for forcings with creatures that are translated into trees. Both lead to new models of the club principle. (shrink)

We analyze the notion of guessing model, a way to assign combinatorial properties to arbitrary regular cardinals. Guessing models can be used, in combination with inaccessibility, to characterize various large cardinal axioms, ranging from supercompactness to rank-to-rank embeddings. The majority of these large cardinal properties can be defined in terms of suitable elementary embeddings j:Vγ→Vλ. One key observation is that such embeddings are uniquely determined by the image structures j[Vγ]≺Vλ. These structures will be the prototypes guessing models. (...) We shall show, using guessing models M, how to prove for the ordinal κM=jM) many of the combinatorial properties that we can prove for the cardinal j) using the structure j[Vγ]≺Vj. κM will always be a regular cardinal, but consistently can be a successor and guessing models M with κM=ℵ2 exist assuming the proper forcing axiom. By means of these models we shall introduce a new structural property of models of PFA: the existence of a “Laver function” f:ℵ2→Hℵ2 sharing the same features of the usual Laver functions f:κ→Hκ provided by a supercompact cardinal κ. Further applications of our analysis will be proofs of the singular cardinal hypothesis and of the failure of the square principle assuming the existence of guessing models. In particular the failure of square shows that the existence of guessing models is a very strong assumption in terms of large cardinal strength. (shrink)

The purpose of this note is to demonstrate that a weak form of club guessing on ω1 implies the existence of an Aronszajn line with no Countryman suborders. An immediate consequence is that the existence of a five element basis for the uncountable linear orders does not follow from the forcing axiom for ω-proper forcings.

Starting with two supercompact cardinals we produce a generic extension of the universe in which a principle that we call GM+ holds. This principle implies ISP and ISP, and hence th...

Popper's methodology does not entail any playing down of the various indispensible distinctions such as the distinction between knowing and guessing, the distinction between myth and science, the distinction between the observational and the theoretical, and between the vernacular and technical sublanguages or technical vocabulary. By avoiding both the totalization that led to the foundationalist position and the scepticist reactions to these frustrated foundationalist hopes, Popper's methodology makes it possible to combine fallibilism with a realist view of theories. It (...) combines the perennial willingness to re-examine positions, statements, etc. with the claim that a particular theory (as an item of knowledge in the objective sense) constitutes cognitive progress over its rivals. However, some of his formulations have been deliberately provocative and in this way have given rise to certain misgivings about possible paradoxical implications, even in philosophers congenial with Popper's approach. The concept of knowledge in the objective sense is, of course, an explicatum which Popper proposes primarily for use in methodology and epistemology. The concept is an expression of the acknowledgment of fallibility in principle. The phrasing that ‘knowledge is conjectural’ or ‘knowledge is fallible’, even when it refers to knowledge in the objective sense, is but an abbreviation for: since our methods for ascertaining the truth-value of a particular statement about empirical reality are fallible in principle, there cannot be any certain knowledge about reality. In everyday life and in politics tolerance will be possible to the extent to which the recognition of this fallibility is more than a declaration. (shrink)

Although the work consists of sixteen connected chapters, there is a difference of motivation that led to the book being published in two volumes. The first eleven chapters, comprising Volume I, attempt to teach good guessing through examples. The remaining chapters, in Volume II, deal with general principles of plausible reasoning.

In [15] we defined and proved the consistency of the principle $\mathrm {GM}^+(\omega _3,\omega _1)$ which implies that many consequences of strong forcing axioms hold simultaneously at $\omega _2$ and $\omega _3$. In this paper we formulate a strengthening of $\mathrm {GM}^+(\omega _3,\omega _1)$ that we call $\mathrm {SGM}^+(\omega _3,\omega _1)$. We also prove, modulo the consistency of two supercompact cardinals, that $\mathrm {SGM}^+(\omega _3,\omega _1)$ is consistent with ZFC. In addition to all the consequences of $\mathrm {GM}^+(\omega _3,\omega _1)$, (...) the principle $\mathrm {SGM}^+(\omega _3,\omega _1)$, together with some mild cardinal arithmetic assumptions that hold in our model, implies that any forcing that adds a new subset of $\omega _2$ either adds a real or collapses some cardinal. This gives a partial answer to a question of Abraham [1] and extends a previous result of Todorčević [16] in this direction. (shrink)

Suppose that λ is the successor of a singular cardinal μ whose cofinality is an uncountable cardinal κ. We give a sufficient condition that the club filter of λ concentrating on the points of cofinality κ is not λ+-saturated.1 The condition is phrased in terms of a notion that we call weak reflection. We discuss various properties of weak reflection. We introduce a weak version of the ♣-principle, which we call ♣*−, and show that if it holds on a (...) stationary subset S of λ, then no normal filter on S is λ+-saturated. Under the above assumptions, ♣*− is true for any stationary subset S of λ which does not contain points of cofinality κ. For stationary sets S which concentrate on points of cofinality κ, we show that ♣*− holds modulo an ideal obtained through the weak reflection. (shrink)

Mark Sagoff has written an engaging and provocative book about the contribution economics can make to environmental policy. Sagoff argues that economics can be helpful in designing institutions and processes through which people can settle environmental disputes. However, he contends that economic analysis fails completely when it attempts to attach value to environmental goods. It fails because preference-satisfaction has no relation to any good. Economic valuation lacks data because preferences cannot be observed. Willingness to pay is benchmarked on market price (...) and thus may reflect producer cost not consumer benefit. Moreover, economists cannot second-guess market outcomes because they have no better information than market participants. Mark Sagoff's conclusion is that environmental policy turns on principles that are best identified and applied through political processes. Written with verve and fluency, this book will be eagerly sought out by students and professionals in environmental policy as well as informed general readers. (shrink)

Legal semiotics is an internationally proliferated subfield of general semiotics. The three-step principles of Peirce’s semiotic logic are the three leading categories: firstness, secondness and thirdness, grounded on the reverse principles of logic: deduction, induction and — Peirce’s discovery — abduction. Neither induction nor abduction can provide a weaker truth claim than deduction. Abduction occurs in intuitive conclusions regarding the possibility of backward reasoning, contrary to the system of law. Civil-law cultures possess an abstract deductive orientation, governed by (...) the rigidity of previous written law, whereas the actual fragility of a common-law system with cases and precedents inclines to induction, orienting its habituality (habits) in moral time and space. Customary law gives credit to abductive values: relevant sentiments, beliefs and propositions are upgraded to valid reasoning. The decision-making by U.S. case law and English common-law is characterized as decision law with abductive undertones. (shrink)

I define a homogeneous \–c.c. proper product forcing for adding many clubs of \ with finite conditions. I use this forcing to build models of \=\aleph _2\), together with \\) and \ large and with very strong failures of club guessing at \.

This paper investigates the principles □λ,δta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square^{{{\rm ta}}}_{\lambda,\delta}}$$\end{document}, weakenings of □λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square_\lambda}$$\end{document} which allow δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\delta}$$\end{document} many clubs at each level but require them to agree on a tail-end. First, we prove that □λ,<ωta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square^{{\rm {ta}}}_{\lambda,< \omega}}$$\end{document} implies □λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square_\lambda}$$\end{document}. (...) Then, by forcing from a model with a measurable cardinal, we show that □λ,2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square_{\lambda,2}}$$\end{document} does not imply □λ,δta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square^{{\rm{ta}}}_{\lambda,\delta}}$$\end{document} for regular λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\lambda}$$\end{document}, and □δ+,δta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square^{{\rm{ta}}}_{\delta^+,\delta}}$$\end{document} does not imply □δ+,<δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square_{\delta^+,< \delta}}$$\end{document}. With a supercompact cardinal the former result can be extended to singular λ, and the latter can be improved to show that □λ,δta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square^{{\rm {ta}}}_{\lambda,\delta}}$$\end{document} does not imply □λ,<δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square_{\lambda,< \delta}}$$\end{document} for δ<λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\delta < \lambda}$$\end{document}. (shrink)

This book presents a history of the correspondence principle from a new perspective. The author provides a unique exploration of the relation between the practice of theory and conceptual development in physics. In the process, he argues for a new understanding of the history of the old quantum theory and the emergence of quantum mechanics. The analysis looks at how the correspondence principle was disseminated and how the principle was applied as a research tool during the 1920s. It provides new (...) insights into the interaction between theoretical tools and scientific problems and shows that the use of this theoretical tool changed the tool itself in a process of transformation through implementation. This process, the author claims, was responsible for the conceptual development of the correspondence principle. This monograph connects to the vast literature in the history of science, which analyzed theoretical practices as based on tacit knowledge, skills, and calculation techniques. It contributes to the historical understanding of quantum physics and the emergence of quantum mechanics. Studying how physicists used a set of tools to solve problems, the author spells out the ‟skillful guessing” that went into the making of quantum theoretical arguments and argues that the integration and implementation of technical resources was a central driving force for the conceptual and theoretical transformation in the old quantum theory. (shrink)

We present a survey of combinatorial set theory relevant to the study of singular cardinals and their successors. The topics covered include diamonds, squares, club guessing, forcing axioms, and PCF theory.

Making a history of the principle of inertia, as of any other principle or concept, is a complex but still possible operation. In this work it has been chosen to make a back story which seemed the most natural way for a reconstruction. On the way back, it has been decided to stop at the 6th century CE with the contribution of Ioannes Philoponus. The principle he stated, although very different from the modern one, is certainly associated with it. Going (...) back in time it is still possible and of course one could proceed to the origins of the homo sapiens who perhaps posed the problem of why a club thrown with his hand could go so far from him. But the similarities that one can find with the modern principle are very vague, too perhaps. Without going so far one could see an embryonic idea of the principle of inertia in the atomistic theory of Democritus in the 5th century BCE. The motion of atoms whirling with no apparent reason can suggest the idea that a body can also move with no reason. But the transition from the atom, a metaphysical being, to the body, an empirical being, is far from immediate. (shrink)

We construct a model satisfying “κ is quasi measurable”. Here, we call κ quasi measurable if there is an ℵ1‐saturated κ‐additive ideal on κ. We also show that, in this model, forcing with adds one but not κ Cohen reals. We introduce a weak club principle and use it to show that, consistently, for some ℵ1‐saturated κ‐additive ideal on κ, forcing with adds one but not κ random reals.

The commentators expressed concerns regarding the relevance and value of non-computational non-symbolic explanations of cognitive performance. But what counts as an “explanation” depends on the pre-theoretical assumptions behind the scenes of empirical science regarding the kinds of variables and relationships that are sought out in the first place, and some of the present disagreements stem from incommensurate assumptions. Traditional cognitive science presumes cognition to be a decomposable system of components interacting according to computational rules to generate cognitive performances (i.e., component-dominant (...) dynamics). We assign primacy to interaction-dominant dynamics among components. Though either choice can be a good guess before the fact, the primacy of interactions is now supported by much recent empirical work in cognitive science. Consequently, in the main, the commentators have failed so far to address the growing evidence corroborating the theory-driven predictions of complexity science. (shrink)

We study combinatorial principles known as stick and club. Several variants of these principles and cardinal invariants connected to them are also considered. We introduce a new kind of side by-side product of partial orderings which we call pseudo-product. Using such products, we give several generic extensions where some of these principles hold together with ¬CH and Martin's axiom for countable p.o.-sets. An iterative version of the pseudo-product is used under an inaccessible cardinal to show the (...) consistency of the club principle for every stationary subset of limits of ω1 together with ¬CH and Martin's axiom for countable p.o.-sets. (shrink)

Given any subset A of ω1 there is a proper partial order which forces that the predicate xA and the predicate xω1A can be expressed by -provably incompatible Σ3 formulas over the structure Hω2,,NSω1. Also, if there is an inaccessible cardinal, then there is a proper partial order which forces the existence of a well-order of Hω2 definable over Hω2,,NSω1 by a provably antisymmetric Σ3 formula with two free variables. The proofs of these results involve a technique for manipulating the (...) guessing properties of club-sequences defined on stationary subsets of ω1 at will in such a way that the Σ3 theory of Hω2,,NSω1 with countable ordinals as parameters is forced to code a prescribed subset of ω1. On the other hand, using theorems due to Woodin it can be shown that, in the presence of sufficiently strong large cardinals, the above results are close to optimal from the point of view of the Levy hierarchy. (shrink)

We revisit several results concerning club principles and nonsaturation of the nonstationary ideal, attempting to improve them in various ways. So we typically deal with a ideal J extending the nonstationary ideal on a regular uncountable cardinal \, our goal being to witness the nonsaturation of J by the existence of towers ).

In lieu of an abstract, here is a brief excerpt of the content:Philosophy and Literature 25.2 (2001) 353-356 [Access article in PDF] Book Review The Metaphysical Club The Metaphysical Club, by Louis Menand; xii & 546 pp. New York: Farrar, Straus and Giroux, 2001, $27.00. "They didn't just want to keep the conversation going; they wanted to get to a better place" (p. 440). So much for the most prominent contemporary pragmatist, Richard Rorty, who remains unmentioned except in (...) the acknowledgments. That better place is participatory democracy (a phrase that does not appear in the book), which "means that everyone is equally in the game, but it also means that no one can opt out" (p. 441). The true name of the game is skeptical tolerance. There are no unquestionable duties or inalienable rights, no immutable natural laws, no absolute moral rules, no highest principles, no inherent virtues, no absolute standards, no stasis, no absolutely certain truth. There are no individual destinies, because the social comes before the individual, and the individual is embedded within and cannot exist without society. Scientific knowledge is always probabilistic, not necessarily because nature is indeterministic, but because we can never know enough to calculate its regularities if they exist. To wit, there are no Platonic Ideas or unchanging universals. All is change, nothing that happens is ever repeated, our general ideas and laws of nature are merely tools for getting along in the world. Above all, ideas do not refer to things, only to other ideas. What expedites our thinking is true. What expedites our acting is right. Whenever we act according to principle, rule, or law, we are making a bet that events will turn out the way [End Page 353] we think they will. If we keep this always in mind, we will never succumb to violence or war in the name of belief or principle. Whatever we believe, it could be otherwise. Such is a general summary of pragmatism as it has filtered down to the textbooks. It is (again befittingly) more or less accurate. The can-do American seeks out cash value in practical life.Oliver Wendell Holmes, Jr., William James, Charles Saunders Pierce, and John Dewey crafted the only indigenous philosophy that has so far been produced in America. Its roots are in Laplacean probability theory, Darwinian evolutionism, and Chauncey Wright's indeterminism. While James hoped to save a place for religion (if it works, go with it) and Pierce a place for God (he thought there had to be a designing intelligence to account for order), the pragmatic result is profoundly skeptical and secular. Neither Holmes nor Dewey thought that individuals imbedded in societies had any need of absolutes. Holmes said that people first decide on the basis of experience, then they deduce. Dewey said that people first behave commonsensically, then they rationalize.There is nothing as condensed as the above in Louis Menand's beautiful book on the ideas, personalities, and influence of Holmes, James, Pierce, and Dewey. I know of no clearer exposition of their ideas, and few biographers have made them come so alive. In particular, Menand's coverage of peripheral (but by no means insignificant) figures is very rich. He describes the development of graduate universities in America in detail from their autocratic beginnings to the institution of academic freedom as we know it today. University presidents, trustees, and administrators are presented luxuriously as the villains, and the professors gloriously as the heroes. Menand remarks with slight amazement that society bought the concept that professors were beholden to the public at large and not to the state or private university owners. He could have commented further on the fact that the concept of academic freedom has become virtually irrelevant in today's corporate research universities."It is a remarkable fact about the United States," Menand begins his book, "that it fought a civil war without undergoing a change in its form of government" (p. ix). This is a breathtaking fact, and I don't suppose Menand had any intent to explain it. "The Civil War swept away the slave civilization of the South, but it swept away almost the whole intellectual... (shrink)

This book presents a theoretical treatment of externalities, public goods, and club goods. The new edition updates and expands the discussion of externalities and their implications, coverage of asymmetric information, underlying game-theoretic formulations, and intuitive and graphical presentations. Aimed at well-prepared undergraduates and graduate students making a serious foray into this branch of economics, the analysis should also interest professional economists wishing to survey recent advances in the field. No other single source for the range of materials explored is (...) currently available. Topics investigated include Nash equilibrium, Lindahl equilibria, club theory, preference-revelation mechanism, Pigouvian taxes, the commons, Coase Theorem, and static and repeated games. The authors use mathematical techniques only as much as necessary to pursue the economic argument. They develop key principles of public economics that are useful for subfields such as public choice, labor economics, economic growth, international economics, environmental and natural resource economics, and industrial organization. (shrink)

Philosophy and economics of Malthusianism. An optimistic view of human population growth and a critique of The Club of Rome and Paul R. Ehrlich, author of The Population Bomb. I apply Julian Simon's perspective to the malthusian debate, inspired by his book The Ultimate Resource. When a child is born he brings into existence not just an extra mouth to feed, but two hands and - more importantly in the long run - an extra brain with which to solve (...) any problems that an increase in population brings. In the long run, and given enough freedom, there in a propensity for humans to produce more than they consume. We are not just like flies in a bottle with a limited amount of resources, but creative creatures that can in principle engage in continual, never ending economic growth. -/- More Info: Multiple publishers: National Review; Clashing Views on Controversial Social Issues; Libertarian Alliance, UK. (shrink)

This paper documents a quantitative study into socially responsible principles and practices adopted in registered clubs in New South Wales Australia to manage one of their social impacts – problem gambling. The survey utilised an adapted version of Aupperle''s (1982) corporate social responsibility instrument to measure the priority given to economic, legal, ethical and discretionary principles in club machine gambling operations. The survey also assessed support for certain management practices in responsible gambling. The results indicate that the (...) participating club managers prioritise economic, legal, ethical and discretionary principles respectively, and that these are statistically related to practices they have implemented and support in responsible gambling. The managers most favoured secondary harm minimisation practices, followed by reactive primary intervention. Less favoured were proactive primary intervention and discretionary practices. These principles and practices contrast markedly with those advocated by key stakeholder groups, as expressed in semi-structured interviews and submissions to the NSW Gaming Inquiry. Non-industry stakeholders favoured a more balanced set of principles and a more holistic set of management practices in responsible gambling. The results also provide validation of Aupperle''s (1982) instrument when applied to corporate management of a single social impact and for Carroll''s (1979, 1991) construct of corporate social responsibility. (shrink)

How can we ensure that players in the National Football League receive excellent health care they can trust from providers who are as free from conflicts of interest as realistically possible? NFL players typically receive care from the club's own medical staff. Club doctors are clearly important stakeholders in player health. They diagnose and treat players for a variety of ailments, physical and mental, while making recommendations to the player concerning those ailments. At the same time, club (...) doctors have obligations to the club, namely to inform and advise clubs about the health status of players. While players and clubs share an interest in player health—both of them want players to be healthy so they can play at peak performance—there are several areas where their interests can diverge, and the divergence presents legal and ethical challenges. The current structure forces club doctors to have obligations to two parties—the club and the player—and to make difficult judgments about when one party's interests must yield to another's. None of the three parties involved should prefer this conflicted approach. We propose to resolve the problem of dual loyalty by largely severing the club doctor's ties with the club and refashioning that role into one of singular loyalty to the player-patient. The main idea is to separate the roles of serving the player and serving the club and replace them with two distinct sets of medical professionals: the Players' Medical Staff and the Club Evaluation Doctor. We begin by explaining the broad ethical principles that guide us and that help shape our recommendation. We then provide a description of the role of the club doctor in the current system. After explaining the concern about the current NFL player health care structure, we provide a recommendation for improving this structure. We then discuss how the club medical staff fits into the broader microenvironment affecting player health. (shrink)

The concept of jointness for guessing principles, specifically ${\diamondsuit _\kappa }$ and various Laver diamonds, is introduced. A family of guessing sequences is joint if the elements of any given sequence of targets may be simultaneously guessed by the members of the family. While equivalent in the case of ${\diamondsuit _\kappa }$, joint Laver diamonds are nontrivial new objects. We give equiconsistency results for most of the large cardinals under consideration and prove sharp separations between joint Laver (...) diamonds of different lengths in the case of θ-supercompact cardinals. (shrink)

We introduce a new method for building models of [Formula: see text], together with [Formula: see text] statements over [Formula: see text], by forcing. Unlike other forcing constructions in the literature, our construction adds new reals, although only [Formula: see text]-many of them. Using this approach, we build a model in which a very strong form of the negation of Club Guessing at [Formula: see text] known as [Formula: see text] holds together with [Formula: see text], thereby answering (...) a well-known question of Moore. This construction can be described as a finite-support weak forcing iteration with side conditions consisting of suitable graphs of sets of models with markers. The [Formula: see text]-preservation is accomplished through the imposition of copying constraints on the information carried by the condition, as dictated by the edges in the graph. (shrink)

In November 1953 after giving his lecture “The Question Concerning Technology” at the Bavarian Academy of Fine Arts, Martin Heidegger wrote in a letter to his wife: “Yet the decisive thing is…the fact that a horizon is opening up amongst the young people, one which announces itself from within technology while going beyond it.” The genesis of Heidegger’s now famous essay occurred 4 years earlier, however, during a series of four lectures delivered on the evening of December 1st, 1949 to (...) a semi-private group of wealthy ship brokers, businessmen, and industry leaders at the Club zu Bremen. The December 1949 lecture would mark Heidegger’s first public speaking engagement since being made an Emeritus Professor at Freiburg University and the institution of a teaching ban as a result of his affiliation with the Nazi party, which, although lifted in 1949, would prevent him from teaching again until the winter semester of 1950–1951. It was at this prestigious Bremen club, in front of an audien .. (shrink)

Our theme is that not every interesting question in set theory is independent of ZFC. We give an example of a first order theory T with countable D(T) which cannot have a universal model at ℵ1 without CH; we prove in ZFC a covering theorem from the hypothesis of the existence of a universal model for some theory; and we prove--again in ZFC--that for a large class of cardinals there is no universal linear order (e.g. in every regular $\aleph_1 < (...) \lambda < 2^{\aleph_0}$). In fact, what we show is that if there is a universal linear order at a regular λ and its existence is not a result of a trivial cardinal arithmetical reason, then λ "resembles" ℵ1--a cardinal for which the consistency of having a universal order is known. As for singular cardinals, we show that for many singular cardinals, if they are not strong limits then they have no universal linear order. As a result of the nonexistence of a universal linear order, we show the nonexistence of universal models for all theories possessing the strict order property (for example, ordered fields and groups, Boolean algebras, p-adic rings and fields, partial orders, models of PA and so on). (shrink)

We give some restrictions for the search for a model of the club principle with no Souslin trees. We show that ${\diamondsuit(2^\omega, [\omega]^\omega}$ , is almost constant on) together with CH and “all Aronszajn trees are special” is consistent relative to ZFC. This implies the analogous result for a double weakening of the club principle.

Assuming $\mathrm{PFA}$, we shall use internally club $\omega _1$ -guessing models as side conditions to show that for every tree T of height $\omega _2$ without cofinal branches, there is a proper and $\aleph _2$ -preserving forcing notion with finite conditions which specialises T. Moreover, the forcing has the $\omega _1$ -approximation property.

In the last few decades, the democratic credentials of global governance institutions have been extensively debated in the fields of international relations and political philosophy. However, despite their prominent role in the architecture of global governance, club governance institutions like the Group of Seven (G7) or the Group of Twenty (G20) have rarely been considered from the perspective of democratic theory. Focussing on the G20, this paper analyses its functions in international political practice and discusses whether, in exercising these (...) functions, the G20 exhibits a democratic deficit. As a standard of democracy, the analysis uses the all-affected principle, according to which all those who are affected by a policy decision should be given the opportunity to participate in decision-making. This paper identifies several democratic shortcomings of the G20, for instance related to the exclusion of citizens of non-member states and a lack of parliamentary and public control. By describing realisable reforms that could to some degree alleviate these shortcomings, it is shown that more democratic institutional alternatives are feasible. Thus, the ascription of a democratic deficit to the G20 is warranted. (shrink)