In this book, Arnold Green discusses the standards that define moral appraisal. Standards assume roles of conduct which can be imposed during socialization only within the traditional family. Otherwise, the basis of order, which is not collective but individual, is undermined by the extreme degree of disaffection we now face. All the panaceas offered, and in some cases enforced, by one intellectual minority or another, will inevitably have a destructive impact upon our communication with one another. Contents: Perception and (...) Ideology; Self and Family; Relativism and the Family Institution; Religion as Vital Force; Social Class and Prejudice. (shrink)

In this paper we show that it is consistent with ZFC that for any set of reals of cardinality the continuum, there is a continuous map from that set onto the closed unit interval. In fact, this holds in the iterated perfect set model. We also show that in this model every set of reals which is always of first category has cardinality less than or equal to ω 1.

We study the preservation of selective covering properties, including classic ones introduced by Menger, Hurewicz, Rothberger, Gerlits and Nagy, and others, under products with some major families of concentrated sets of reals.Our methods include the projection method introduced by the authors in an earlier work, as well as several new methods. Some special consequences of our main results are : Every product of a concentrated space with a Hurewicz S1S1 space satisfies S1S1. On the other hand, assuming the Continuum Hypothesis, (...) for each Sierpiński set S there is a Luzin set L such that L×SL×S can be mapped onto the real line by a Borel function. Assuming Semifilter Trichotomy, every concentrated space is productively Menger and productively Rothberger. Every scale set is productively Hurewicz, productively Menger, productively Scheepers, and productively Gerlits–Nagy. Assuming d=ℵ1d=ℵ1, every productively Lindelöf space is productively Hurewicz, productively Menger, and productively Scheepers.A notorious open problem asks whether the additivity of Rothberger's property may be strictly greater than addadd, the additivity of the ideal of Lebesgue-null sets of reals. We obtain a positive answer, modulo the consistency of Semifilter Trichotomy >ℵ1.Our results improve upon and unify a number of results, established earlier by many authors. (shrink)

We show that there is a model of ZF in which the Borel hierarchy on the reals has length ω2. This implies that ω1 has countable cofinality, so the axiom of choice fails very badly in our model. A similar argument produces models of ZF in which the Borel hierarchy has exactly λ + 1 levels for any given limit ordinal λ less than ω2. We also show that assuming a large cardinal hypothesis there are models of ZF in which (...) the Borel hierarchy is arbitrarily long. (shrink)

Let κ B be the least cardinal for which the Baire category theorem fails for the real line R. Thus κ B is the least κ such that the real line can be covered by κ many nowhere dense sets. It is shown that κ B cannot have countable cofinality. On the other hand it is consistent that the corresponding cardinal for 2 ω 1 be ℵ ω . Similar questions are considered for the ideal of measure zero sets, other (...) ω 1 saturated ideals, and the ideal of zero-dimensional subsets of R ω 1. (shrink)

In this paper we ask the question: to what extent do basic set theoretic properties of Loeb measure depend on the nonstandard universe and on properties of the model of set theory in which it lies? We show that, assuming Martin's axiom and κ-saturation, the smallest cover by Loeb measure zero sets must have cardinality less than κ. In contrast to this we show that the additivity of Loeb measure cannot be greater than ω 1 . Define $\operatorname{cof}(H)$ as the (...) smallest cardinality of a family of Loeb measure zero sets which cover every other Loeb measure zero set. We show that $\operatorname{card}(\lfloor\log_2(H)\rfloor) \leq \operatorname{cof}(H) \leq \operatorname{card}(2^H)$ , where card is the external cardinality. We answer a question of Paris and Mills concerning cuts in nonstandard models of number theory. We also present a pair of nonstandard universes $M \preccurlyeq N$ and hyperfinite integer H ∈ M such that H is not enlarged by N, 2 H contains new elements, but every new subset of H has Loeb measure zero. We show that it is consistent that there exists a Sierpiński set in the reals but no Loeb-Sierpiński set in any nonstandard universe. We also show that it is consistent with the failure of the continuum hypothesis that Loeb-Sierpiński sets can exist in some nonstandard universes and even in an ultrapower of a standard universe. (shrink)

In this paper we prove three theorems about the theory of Borel sets in models of ZF without any form of the axiom of choice. We prove that if \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${B\subseteq 2^\omega}$$\end{document} is a Gδσ-set then either B is countable or B contains a perfect subset. Second, we prove that if 2ω is the countable union of countable sets, then there exists an Fσδ set \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} (...) \setlength{\oddsidemargin}{-69pt} \begin{document}$${C\subseteq 2^\omega}$$\end{document} such that C is uncountable but contains no perfect subset. Finally, we construct a model of ZF in which we have an infinite Dedekind finite \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${D\subseteq 2^\omega}$$\end{document} which is Fσδ. (shrink)

In this paper we will consider two possible definitions of projective subsets of a separable metric space X. A set A subset of or equal to X is Σ11 iff there exists a complete separable metric space Y and Borel set B subset of or equal to X × Y such that A = {x ε X : there existsy ε Y ε B}. Except for the fact that X may not be completely metrizable, this is the classical definition of (...) analytic set and hence has many equivalent definitions, for example, A is Σ11 iff A is relatively analytic in X, i.e., A is the restriction to X of an analytic set in the completion of X. Another definition of projective we denote by ΣX1 or abstract projective subset of X. A set of A subset of or equal to X is ΣX1 iff there exists an n ε ω and a Borel set B subset of or equal to X × Xn such that A = {x ε X:there existsy ε Xn ε B}. These sets ca n be far more pathological. While the family of sets Σ11 is closed under countable intersections and countable unions, there is a consistent example of a separable metric space X where ΣX1 is not closed under countable intersections or countable unions. This takes place in the Cohen real model. Assuming CH, there exists a separable metric space X such that every Σ11 set is Borel in X but there exists a Σ11 set which is not Borel in X2. The space X2 has Borel subsets of arbitrarily large rank while X has bounded Borel rank. This space is a Luzin set and the technique used here is Steel forcing with tagged trees. We give examples of spaces X illustrating the relationship between Σ11 and ΣX1 and give some consistent examples partially answering an abstract projective hierarchy problem of Ulam. (shrink)

Abstract.In this paper we prove that it is consistent that every γ-set is countable while not every strong measure zero set is countable. We also show that it is consistent that every strong γ-set is countable while not every γ-set is countable. On the other hand we show that every strong measure zero set is countable iff every set with the Rothberger property is countable.

For a Polish group let be the minimal number of translates of a fixed closed nowhere dense subset of required to cover . For many locally compact this cardinal is known to be consistently larger than which is the smallest cardinality of a covering of the real line by meagre sets. It is shown that for several non-locally compact groups . For example the equality holds for the group of permutations of the integers, the additive group of a separable Banach (...) space with an unconditional basis and the group of homeomorphisms of various compact spaces. (shrink)

The slow emergence of Dalton's chemical atomic theory has long been a considerable puzzle to historians of science The lengthy delay between Dalton's early work on mixed gases and particle weights and the eventual publication of the first part of his New System of Chemical Philosophy has called forth a variety of explanations. It is now more than half a century since A. N. Meldrum stressed“…the efforts Dalton had to make, in order to arouse attention to the importance of his (...) ideas regarding atoms. For some nine years , if not longer, he endeavoured to spread abroad his ideas, both by private communications and publicly, by his writings and by lectures in various parts of the country…“Dalton's chemical theory was formed by the 6th September 1803, and he proceeded forthwith to extend and apply it, and make it known in every direction…”And though Meldrum's view is now no longer accepted, no systematic and detailed account of Dalton's activities over these years is available to replace Meldrum's assertions. (shrink)

Even if we recognize that the delta-lognormal model provides an excellent fit to a large variety of data, the question remains as to what we actually learn from such a model, which could be seen as merely another multiparameter account? Do we welcome such an encompassing account, or do we expect to learn more from the limitations that become apparent when applying dedicated models addressing specific classes of movements?

In this paper we study the question assuming MA+⌝CH does Sacks forcing or Laver forcing collapse cardinals? We show that this question is equivalent to the question of what is the additivity of Marczewski's ideals 0. We give a proof that it is consistent that Sacks forcing collapses cardinals. On the other hand we show that Laver forcing does not collapse cardinals.

Define z to be the smallest cardinality of a function f: X → Y with X. Y ⊆ 2ω such that there is no Borel function g ⊇ f. In this paper we prove that it is relatively consistent with ZFC to have b < z where b is, as usual, smallest cardinality of an unbounded family in ωω. This answers a question raised by Zapletal. We also show that it is relatively consistent with ZFC that there exists X ⊆ (...) 2ω such that the Borel order of X is bounded but there exists a relatively analytic subset of X which is not relatively coanalytic. This answers a question of Mauldin. (shrink)

Leading Particular Baptist theologian Benjamin Keach came to prominence just as an antitrinitarian theology native to England gained a stronghold. What had previously been deemed off-limits by the Establishment became a commonplace by the end of the seventeenth century based on a strict biblicism that eschewed the extra-biblical language of trinitarian orthodoxy. As one who considered himself a strong biblicist, Keach deftly maneuvered his theological writings between what he saw as two extremes: the one that refused to consider any language (...) that moved beyond the mere words of scripture, represented by many of his General Baptist contemporaries and the other that over-emphasized the role of tradition with no eye toward biblical truth, represented by the Roman Catholics. Keach’s explication of trinitarianism demonstrated that these two extremes did not have to be seen as competing with each other. Instead, the correct understanding of the Bible included ‘the just and necessary consequences’ that could be deduced from Scripture, and the ‘universal tradition’ aided the pastor theologian in ascertaining the truth. The result, for Keach and his audience, was an ancient view of trinitarianism that offered a way of peace between the the two extremes vying for the public ear in the late seventeenth century. (shrink)

We say that $\mathcal {I}$ is an ideal independent family if no element of ${\mathcal {I}}$ is a subset mod finite of a union of finitely many other elements of ${\mathcal {I}}.$ We will show that the minimum size of a maximal ideal independent family is consistently bigger than both $\mathfrak {d}$ and $\mathfrak {u},$ this answers a question of Donald Monk.

We consider a well-known partial order of Prikry for producing a collapsing function of minimal degree. Assuming MA + ≠ CH, every new real constructs the collapsing map.

The Axiom of Projective Determinacy implies the existence of a universal $\utilde{\Pi}^{1}_{n}\setminus\utilde{\Delta}^{1}_{n}$ set for every $n \geq 1$. Assuming $\text{\upshape MA}(\aleph_{1})+\aleph_{1}=\aleph_{1}^{\mathbb{L}}$ there exists a universal $\utilde{\Pi}^{1}_{1}\setminus\utilde{\Delta}^{1}_{1}$ set. In ZFC there is a universal $\utilde{\Pi}^{0}_{\alpha}\setminus\utilde{\Delta}^{0}_{\alpha}$ set for every $\alpha$.

The ease with which genotyping technologies generate tremendous amounts of data on research participants has been well chronicled, a feat that continues to become both faster and cheaper to perform. In parallel to these advances come additional ethical considerations and debates, one of which centers on providing individual research results and incidental findings back to research participants taking part in genetic research efforts. In 2006 the Industry Pharmacogenomics Working Group offered some ‘Points-to-Consider’ on this topic within the context of the (...) drug development process from those who are affiliated to pharmaceutical companies. Today many of these points remain applicable to the discussion but will be expanded upon in this updated viewpoint from the I-PWG. The exploratory nature of pharmacogenomic work in the pharmaceutical industry is discussed to provide context for why these results typically are not best suited for return. Operational challenges unique to this industry which cause barriers to returning this information are also explained. (shrink)

Effective Altruism is a movement and a philosophy that has reinvigorated the debate about the nature of beneficence. At base, it is the consistent application of microeconomic principles to beneficent action. The movement has exposed that many forms of giving do little good (or do active harm), but others do tremendous good. Questioning Beneficence uses Effective Altruism as a launchpad to ask hard questions about beneficence more generally. Must we be Effective Altruists, or is Effective Altruism and the ideas driving (...) the movement a mistake? How much should we give and-if anything-how should we give it? What are the respective roles of different kinds of institutions? Is charity anti-democratic and do billionaire philanthropists have too much power? Is Effective Altruism just utilitarianism in disguise? Questioning Beneficence is written by four philosophers, each with distinct points of view. It introduces a new standard for debating ideas in philosophy as each author poses and answers three questions and each of his three co-authors responds to those questions in turn. Finally, the first author replies to his co-authors' responses. Throughout the book, there is a spirit of curiosity, intellectual risk taking, and truth-seeking, rather than point-scoring and one-upsmanship. Questioning Beneficence demonstrates what open-minded, real dialogue over an important issue can be at its very best. (shrink)

This collection of "comparisons and contrasts" explores Heinz Kohut's self psychology in relation to a wide-ranging group of modern thinkers, both inside and outside of analysis. Separate sections analyze self psychology alongside Freud and the first generation of psychoanalytic dissidents; British object relations theorists; and contemporary theorists like Kernberg, Mahler, Lacan, and Masterson.

DNA methylation is a repressive epigenetic modification that is essential for development and its disruption is widely implicated in disease. Yet, remarkably, ablation of DNA methylation in transgenic mouse models has limited impact on transcriptional states. Across multiple tissues and developmental contexts, the predominant transcriptional signature upon loss of DNA methylation is the de‐repression of a subset of germline genes, normally expressed in gametogenesis. We recently reported loss of de novo DNA methyltransferase DNMT3B resulted in up‐regulation of germline genes and (...) impaired syncytiotrophoblast formation in the murine placenta. This defect led to embryonic lethality. We hypothesize that de‐repression of germline genes in the Dnmt3b knockout underpins aspects of the placental phenotype by interfering with normal developmental processes. Specifically, we discuss molecular mechanisms by which aberrant expression of the piRNA pathway, meiotic proteins or germline transcriptional regulators may disrupt syncytiotrophoblast development. (shrink)