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)

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 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)

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

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.

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)

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)

Let n ≥ 3 be an integer. We show that it is consistent (relative to the consistency of n - 2 strong cardinals) that every $\Sigma_n^1-set$ of reals is universally Baire yet there is a (lightface) projective well-ordering of the reals. The proof uses "David's trick" in the presence of inner models with strong cardinals.

Jan Narveson criticizes the view expressed in my Libertarian Philosophy in the Real World that there is no orthodox libertarian position on the ethics of abortion. He asserts that fetuses lack the defining characteristics of personhood, and thus are ineligible for what he terms “intrinsic” rights under his, and presumably any other, plausible libertarian theory. My counterargument is threefold: Narveson’s contractarianism can be interpreted in a way that is consistent with the pro-life perspective; because his theory permits no principled distinction (...) between the moral status of third trimester fetuses and newborns, the contrary reading of his social contract produces a result that is implausible and even repellent; and even if his version of contractarianism does imply a unique, aggressively pro-choice stance on abortion, there are competing libertarian theories that are receptive to pro-life views. (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)

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.

Let n ≥ 3 be an integer. We show that it is consistent that every σ1n-set of reals is universally Baire yet there is a projective well-ordering of the reals. The proof uses “David’s trick” in the presence of inner models with strong cardinals.

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.

Trisomy 13 and 18 are rare chromosomal abnormalities associated with high morbidity and mortality. Improved survival rates and increased prevalence of aggressive medical intervention have resulted in families and physicians holding different perspectives regarding the appropriate management of children with T 13/18. Families were invited for open-ended interviews regarding their experiences with the medical care of a child with T 13/18 over the past 5 years. Seven of 33 invited families were surveyed; those who had spent more than 40 days (...) in the hospital were most likely to accept the invitation. Grounded theory technique was used to analyze the interviews. This method elicited four key themes regarding family perspectives on children with T 13/18: they are unique and significant, they transform the lives of others, their families can feel overwhelmed and powerless in the medical setting, their families are motivated to “carry the torch” and tell their story. Families also emphasized ways in which Internet support groups can provide both positive and negative perspectives. The ensuing discussion explores the difficulties of parents and physicians in forecasting the impact that T 13/18 will have on families and emphasizes a narrative approach to elicit a map of the things that matter to them. The paper concludes that while over-reliance on dire prognostic data can alienate families, examining the voice, character and plot of patient stories can be a powerful way for physicians to foster shared decision-making with families. (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)

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)

This essay argues that the affective component inherent in the enthymeme is the essence of aristotle's concept of the enthymeme as practical reasoning. 'affective component' refers to emotions and feelings. The three proofs of the thesis are the etymology of 'enthymeme', Aristotle's works on human action and practical wisdom, And aristotle's rhetoric. These sources show the inherent relation between enthymemes and phronesis, Or practical reasoning, Not nous, Or abstract intellect.

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)

There is widespread agreement among large segments of western society that we are living in a period of hard times. At first glance such a belief might seem exceedingly odd. After all, persons in western society find themselves living in a time of unprecedented material abundance. Hunger and disease, evils all too familiar to the members of earlier generations, although far from eradicated from modern life, are plainly on the wane. Persons alive today can look forward to healthier, longer, and (...) more comfortable lives than those of their grand parents. Nevertheless, the feeling that life today is especially difficult is rampant in government, in the media, in popular books, and in academic circles. Western society is perceived in many quarters as wracked by crises of all sorts-of faith, of power, of authority, of social turmoil, of declining quality in workmanship and products, and of a general intellectual malaise afflicting both those on the Left and the Right. A tone of crisis permeates the language of public life. Editorials in major newspapers are full of dire warnings about the dangers of unbridled egoism, avarice and greed, and the risks and horrors of pollution, overpopulation, the arms race, crime, and indulgent lifestyles. (shrink)