The Fraenkel-Mostowski method has been widely used to prove independence results among weak versions of the axiom of choice. In this paper it is shown that certain statements cannot be proved by this method. More specifically it is shown that in all Fraenkel-Mostowski models the following hold: 1. The axiom of choice for sets of finite sets implies the axiom of choice for sets of well-orderable sets. 2. The Boolean prime ideal theorem implies a weakened form of Sikorski's theorem.
Let NBG be von Neumann-Bernays-Gödel set theory without the axiom of choice and let NBGA be the modification which allows atoms. In this paper we consider some of the well-known class or global forms of the wellordering theorem, the axiom of choice, and maximal principles which are known to be equivalent in NBG and show they are not equivalent in NBGA.
This is a continuation of . We study the Tychonoff Compactness Theorem for various definitions of compactness and for various types of spaces . We also study well ordered Tychonoff products and the effect that the multiple choice axiom has on such products.
We show that it is not possible to construct a Fraenkel-Mostowski model in which the axiom of choice for well-ordered families of sets and the axiom of choice for sets are both true, but the axiom of choice is false.
We study statements about countable and well-ordered unions and their relation to each other and to countable and well-ordered forms of the axiom of choice. Using WO as an abbreviation for “well-orderable”, here are two typical results: The assertion that every WO family of countable sets has a WO union does not imply that every countable family of WO sets has a WO union; the axiom of choice for WO families of WO sets does not imply that the countable union (...) of countable sets is WO. (shrink)
Two Fraenkel-Mostowski models are constructed in which the Boolean Prime Ideal Theorem is true. In both models, AC for countable sets is true, but AC for sets of cardinality 2math image and the 2m = m principle are both false. The Principle of Dependent Choices is true in the first model, but false in the second.
In Zermelo-Fraenkel set theory with the axiom of choice every set has the same cardinal number as some ordinal. Von Rimscha has weakened this condition to “Every set has the same cardinal number as some transitive set”. In set theory without the axiom of choice, we study the deductive strength of this and similar statements introduced by von Rimscha.
We investigate the set theoretical strength of some properties of normality, including Urysohn's Lemma, Tietze-Urysohn Extension Theorem, normality of disjoint unions of normal spaces, and normality of Fσ subsets of normal spaces.
The apolipoprotein E gene plays an important role in the pathogenesis of Alzheimer's disease , and amyloid plaque comprised mostly of the amyloid-beta peptide ) is one of the major hallmarks of AD. However, the relationship between these two important molecules is poorly understood. We examined how A treatment affects APOE expression in cultured cells and tested the role of the transcription factor NF-B in APOE gene regulation. To delineate NF-B's role, we have characterized a 1098 nucleotide segment containing the (...) 5'-flanking region of the human APOE gene . Sequence analysis of this region suggests the presence of two potential NF-B elements. To demonstrate promoter activity, the region was cloned upstream of a promoterless luciferase gene. This segment was able to drive expression of luciferase in transient transfections of human fetal glial cells. Promoter activity was stimulated twofold by A treatment. Pretreatment with double-stranded DNA decoy oligonucleotides against NF-B reduced A stimulation. Deletion and mutagenetic analyses demonstrated that the distal NF-B element was functional and showed a strong DNA-protein complex band in gel shift analysis, similar to that from control NF-B consensus element. An anti-inflammatory and anti-NF-B drug, sodium salicylate, significantly blocked A-induced APOE promoter function. Our data provide evidence that upregulation of APOE by A in astroglial cells is mediated by an NF-B-element present in the 5'-flanking region of the APOE gene. (shrink)
This is Volume I of a new series entitled Aquinas Scripture Commentaries. With the exception of the nineteenth century Oxford translation of Aquinas' Gospel Commentaries, Aquinas the exegete has not been available in English. It is hoped that this Magi Books series will fill this gap soon, though no definite prospectus of further titles other than this and the one mentioned below has been set forth by the publisher. Aquinas' Scripture Commentaries, like his Commentaries on the Aristotelian corpus, follow the (...) lectio form of line by line and structural interpretation of the entire text. This literal approach to Biblical exegesis is mediated, however, by the systematic philosophical and theological perspective Aquinas brings to bear on the text. The result of this union is a Commentary which has quite a bit more than simply historical importance. The translation is smooth and the book has been turned out in a reasonably scholarly fashion.—E. A. R. (shrink)
O presente artigo, analisando a hermenêutica de Gadamer e a teoria crítica de Horkheimer e Marcuse, procura mostrar que, se se concebe a sociedade moderna do ponto de vista do político, é possível elaborar uma teoria da modernidade em que ambas, em vez de se oporem, sejam complementares.This paper analyses Gadamer's hermeneutics and the critical theory of Horkheimer and Marcuse. It tries to show that, if modern society is conceived as political, then it is possible to elaborate a theory of (...) modernity where hermeneutics and critical theory, instead of opposing, complement each other. (shrink)
Selections from "twentieth century sources" which include Moore, Broad, Price, Paul, Lewis, Chisholm, and Warnock. Sense data and phenomenalism are the most heavily represented topics. The choice is substantial, and the editor has skillfully arranged selections in pairs which take up opposite sides of the same problem. This appears to be the best buy in paper on this subject.—E. A. R.