We develop a new method for coding sets while preserving GCH in the presence of large cardinals, particularly supercompact cardinals. We will use the number of normal measures carried by a measurable cardinal as an oracle, and therefore, in order to code a subset A of κ, we require that our model contain κ many measurable cardinals above κ. Additionally we will describe some of the applications of this result. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

We explore Woodin's Universality Theorem and consider to what extent large cardinal properties are transferred into HOD (and other inner models). We also separate the concepts of supercompactness, supercompactness in HOD and being HOD-supercompact. For example, we produce a model where a proper class of supercompact cardinals are not HOD-supercompact but are supercompact in HOD. Additionally we introduce a way to measure the degree of HOD-supercompactness of a supercompact cardinal, and we develop methods to control these degrees simultaneously for a (...) proper class of supercompact cardinals. Finally, we also produce a model in which the unique supercompact cardinal is also the only strongly compact cardinal, no cardinal is supercompact up to an inaccessible cardinal, level by level inequivalence holds and the unique supercompact cardinal is not HOD-supercompact. (shrink)

We explore the consistency strength of Σ 3 1 and Σ 4 1 absoluteness, for a variety of forcing notions.

We present a new partial order for directly forcing morasses to exist that enjoys a significant homogeneity property. We then use this forcing in a reverse Easton iteration to obtain an extension universe with morasses at every regular uncountable cardinal, while preserving all n-superstrong , hyperstrong and 1-extendible cardinals. In the latter case, a preliminary forcing to make the GCH hold is required. Our forcing yields morasses that satisfy an extra property related to the homogeneity of the partial order; we (...) refer to them as mangroves and prove that their existence is equivalent to the existence of morasses. Finally, we exhibit a partial order that forces universal morasses to exist at every regular uncountable cardinal, and use this to show that universal morasses are consistent with n-superstrong, hyperstrong, and 1-extendible cardinals. This all contributes to the second author’s outer model programme, the aim of which is to show that L-like principles can hold in outer models which nevertheless contain large cardinals. (shrink)

Let X be a set, and let $\hat{X} = \bigcup^\infty_{n = 0} X_n$ be the superstructure of X, where X 0 = X and X n + 1 = X n ∪ P(X n ) (P(X) is the power set of X) for n ∈ ω. The set X is called a flat set if and only if $X \neq \varnothing.\varnothing \not\in X.x \cap \hat X = \varnothing$ for each x ∈ X, and $x \cap \hat{y} = \varnothing$ for x.y (...) ∈ X such that x ≠ y, where $\hat{y} = \bigcup^\infty_{n = 0} y_n$ is the superstructure of y. In this article, it is shown that there exists a bijection of any nonempty set onto a flat set. Also, if W̃ is an ultrapower of X̂ (generated by any infinite set I and any nonprincipal ultrafilter on I), it is shown that W̃ is a nonstandard model of X: i.e., the Transfer Principle holds for X̂ and W̃, if X is a flat set. Indeed, it is obvious that W̃ is not a nonstandard model of X when X is an infinite ordinal number. The construction of flat sets only requires the ZF axioms of set theory. Therefore, the assumption that X is a set of individuals (i.e., $x \neq \varnothing$ and a ∈ x does not hold for x ∈ X and for any element a) is not needed for W̃ to be a nonstandard model of X. (shrink)

Although virtually all comparative research about risk perception focuses on which hazards are of concern to people in different culture groups, much can be gained by focusing on predictors of levels of risk perception in various countries and places. In this case, we examine standard and novel predictors of risk perception in seven sites among communities affected by a flood in Mexico (one site) and volcanic eruptions in Mexico (one site) and Ecuador (five sites). We conducted more than 450 interviews (...) with questions about how people feel at the time (after the disaster) regarding what happened in the past, their current concerns, and their expectations for the future. We explore how aspects of the context in which people live have an effect on how strongly people perceive natural hazards in relationship with demographic, well-being, and social network factors. Generally, our research indicates that levels of risk perception for past, present, and future aspects of a specific hazard are similar across these two countries and seven sites. However, these contexts produced different predictors of risk perception—in other words, there was little overlap between sites in the variables that predicted the past, present, or future aspects of risk perception in each site. Generally, current stress was related to perception of past danger of an event in the Mexican sites, but not in Ecuador; network variables were mainly important for perception of past danger (rather than future or present danger), although specific network correlates varied from site to site across the countries. (shrink)

Advancements in artificial intelligence and (social) robotics raise pertinent questions as to how these technologies may help shape the society of the future. The main aim of the chapter is to consider the social and conceptual disruptions that might be associated with social robots, and humanoid social robots in particular. This chapter starts by comparing the concepts of robots and artificial intelligence and briefly explores the origins of these expressions. It then explains the definition of a social robot, as well (...) as the definition of humanoid robots. A key notion in this context is the idea of anthropomorphism: the human tendency to attribute human qualities, not only to our fellow human beings, but also to parts of nature and to technologies. This tendency to anthropomorphize technologies by responding to and interacting with them as if they have human qualities is one of the reasons why social robots (in particular social robots designed to look and behave like human beings) can be socially disruptive. As is explained in the chapter, while some ethics researchers believe that anthropomorphization is a mistake that can lead to various forms of deception, others — including both ethics researchers and social roboticists — believe it can be useful or fitting to treat robots in anthropomorphizing ways. The chapter explores that disagreement by, among other things, considering recent philosophical debates about whether social robots can be moral patients, that is, whether it can make sense to treat them with moral consideration. Where one stands on this issue will depend either on one’s views about whether social robots can have, imitate, or represent morally relevant properties, or on how people relate to social robots in their interactions with them. Lastly, the chapter urges that the ethics of social robots should explore intercultural perspectives, and highlights some recent research on Ubuntu ethics and social robots. (shrink)

We present here an approach to the fine structure of L based solely on elementary model theoretic ideas, and illustrate its use in a proof of Global Square in L. We thereby avoid the Lévy hierarchy of formulas and the subtleties of master codes and projecta, introduced by Jensen [3] in the original form of the theory. Our theory could appropriately be called ”Hyperfine Structure Theory”, as we make use of a hierarchy of structures and hull operations which refines the (...) traditional Lα -or Jα-sequences with their Σn-hull operations.§1. Introduction. In 1938, K. Gödel defined the model L of set theory to show the relative consistency of Cantor's Continuum Hypothesis. L is defined as a unionof initial segments which satisfy: L0 = ∅, Lλ = ∪α<λLα for limit ordinals λ, and, crucially, Lα + 1 = the collection of 1st order definable subsets of Lα. Since every transitive model of set theory must be closed under 1st order definability, L turns out to be the smallest inner model of set theory. Thus it occupies the central place in the set theoretic spectrum of models.The proof of the continuum hypothesis in L is based on the very uniform hierarchical definition of the L-hierarchy. The Condensation Lemma states that if π : M → Lα is an elementary embedding, M transitive, then some ; the lemma can be proved by induction on α. If a real, i.e., a subset of ω, is definable over some Lα,then by a Löwenheim-Skolem argument it is definable over some countable M as above, and hence over some, < ω1. This allows one to list the reals in L in length ω1 and therefore proves the Continuum Hypothesis in L. (shrink)

The Infinite Time Turing Machine model [8] of Hamkins and Kidder is, in an essential sense, a "Σ₂-machine" in that it uses a Σ₂ Liminf Rule to determine cell values at limit stages of time. We give a generalisation of these machines with an appropriate Σ n rule. Such machines either halt or enter an infinite loop by stage ζ(n) = df μζ(n)[∃Σ(n) > ζ(n) L ζ(n) ≺ Σn L Σ(n) ], again generalising precisely the ITTM case. The collection of (...) such machines taken together computes precisely those reals of the least model of analysis. (shrink)

Arthur Danto is the Johnsonian Professor Emeritus of Philosophy at Columbia University and the most influential philosopher of art in the last half century. As an art critic for The Nation for 25 years and frequent contributor to other widely read outlets such as the New York Review of Books, Danto also has become one of the most respected public intellectuals of his generation. He is the author of some two dozen important books, along with hundreds of articles and (...) reviews which have been the center of both controversy and discussion. In this volume Danto offers his intellectual autobiography and responds to essays by 27 of the keenest critics of his thought from the worlds of philosophy and the arts. The book includes 16 pages of color art reproductions. Danto is the author dozens of books on art, philosophy, the philosophy of art, and art criticism. He is a rare philosopher who is also a public intellectual. (shrink)

Over the past forty years, the health humanities, previously called the medical humanities, has emerged as one of the most exciting fields for interdisciplinary scholarship, advancing humanistic inquiry into bioethics, human rights, health care, and the uses of technology. It has also helped inspire medical practitioners to engage in deeper reflection about the human elements of their practice. In _Health Humanities Reader_, editors Therese Jones, Delese Wear, and Lester D. Friedman have assembled fifty-four leading scholars, educators, artists, and clinicians (...) to survey the rich body of work that has already emerged from the field—and to imagine fresh approaches to the health humanities in these original essays. The collection’s contributors reflect the extraordinary diversity of the field, including scholars from the disciplines of disability studies, history, literature, nursing, religion, narrative medicine, philosophy, bioethics, medicine, and the social sciences. With warmth and humor, critical acumen and ethical insight, _Health Humanities Reader_ truly humanizes the field of medicine. Its accessible language and broad scope offers something for everyone from the experienced medical professional to a reader interested in health and illness. (shrink)

A classic result of Baumgartner-Harrington-Kleinberg [1] implies that assuming CH a stationary subset of ω1 has a CUB subset in a cardinal-perserving generic extension of V, via a forcing of cardinality ω1. Therefore, assuming that $\omega_2^L$ is countable: { $X \in L \mid X \subseteq \omega_1^L$ and X has a CUB subset in a cardinal -preserving extension of L} is constructible, as it equals the set of constructible subsets of $\omega_1^L$ which in L are stationary. Is there a similar such (...) result for subsets of $\ omega_2^L$ ? Building on work of M. Stanley [9], we show that there is not. We shall also consider a number of related problems, examining the extent to which they are "solvable" in the above sense, as well as defining a notion of reduction between them. (shrink)

This article describes the evolution of extra-mural team projects in the Wharton School's new MBA curriculum, emphasizing both the benefits of doing community service and the value these projects have in providing real work opportunities for learning teams; five- or six-person student groups that do collective tasks in Foundations of Leadership and other required courses throughout the first of a two-year program.

In recent years higher recursion theory has experienced a deep interaction with other areas of logic, particularly set theory (fine structure, forcing, and combinatorics) and infinitary model theory. In this paper we wish to illustrate this interaction by surveying the progress that has been made in two areas: the global theory of the κ-degrees and the study of closure ordinals.

If A is an admissible set, let HC(A) = {x∣ x ∈ A and x is hereditarily countable in A}. Then HC(A) is admissible. Corollaries are drawn characterizing the "real parts" of admissible sets and the analytical consequences of admissible set theory.

Jensen's remarkable Coding Theorem asserts that the universe can be included in L[R] for some real R, via class forcing. The purpose of this article is to present a simpler proof of Jensen's theorem, obtained by implementing some changes first developed for the theory of Strong Coding. In particular, our proof avoids the split into cases, according to whether or not 0# exists in the ground model.

We characterize the classifiability of a countable first-order theory T in terms of the solvability of the potential-isomorphism problem for models of T.

We isolate a condition on a class A of ordinals sufficient to Δ1-code it by a real in a class-generic extension of L. We then apply this condition to show that the class of ordinals of L-cofinality ω is Δ1 in a real of L-degree strictly below O#.

We establish the equiconsistency of a simple statement in definability theory with the failure of the GCH at all infinite cardinals. The latter was shown by Foreman and Woodin to be consistent, relative to the existence of large cardinals.