✦ LIBER ✦

RUSSELL'S ALTERNATIVE TO THE AXIOM OF CHOICE

✍ Scribed by Norbert Brunner; Paul Howard

Publisher: John Wiley and Sons
Year: 1992
Tongue: English
Weight: 305 KB
Volume: 38
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.19920380149

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

We prove the independence of some weakenings of the axiom of choice related to the question if the unions of wellorderable families of wellordered sets are wellorderable.

📜 SIMILAR VOLUMES

The Induction Axiom and the Axiom of Cho

The Induction Axiom and the Axiom of Choice

✍ B. Germansky 📂 Article 📅 1961 🏛 John Wiley and Sons 🌐 English ⚖ 326 KB 👁 1 views

Unions and the axiom of choice

✍ Omar De la Cruz; Eric J. Hall; Paul Howard; Kyriakos Keremedis; Jean E. Rubin 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 176 KB 👁 1 views

## Abstract 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 se

Arrow's Theorem, Weglorz' Models and the

Arrow's Theorem, Weglorz' Models and the Axiom of Choice

✍ Norbert Brunner; H. Reiju Mihara 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 342 KB 👁 2 views

Metric spaces and the axiom of choice

✍ Omar De la Cruz; Eric Hall; Paul Howard; Kyriakos Keremedis; Jean E. Rubin 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 173 KB 👁 1 views

## Abstract We study conditions for a topological space to be metrizable, properties of metrizable spaces, and the role the axiom of choice plays in these matters.

Extending Independent Sets to Bases and

Extending Independent Sets to Bases and the Axiom of Choice

✍ Kyriakos Keremedis 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 363 KB 👁 1 views

## Abstract We show that the both assertions “in every vector space __B__ over a finite element field every subspace __V__ ⊆ __B__ has a complementary subspace __S__” and “for every family 𝒜 of disjoint odd sized sets there exists a subfamily ℱ={F~j~:j ϵω} with a choice function” together imply the

TWO TOPOLOGICAL EQUIVALENTS OF THE AXIOM

TWO TOPOLOGICAL EQUIVALENTS OF THE AXIOM OF CHOICE

✍ Eric Schechter; E. Schechter 📂 Article 📅 1992 🏛 John Wiley and Sons 🌐 English ⚖ 159 KB 👁 1 views

## Abstract We show that the Axiom of Choice is equivalent to each of the following statements: (i) A product of closures of subsets of topological spaces is equal to the closure of their product (in the product topology); (ii) A product of complete uniform spaces is complete.