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The Induction Axiom and the Axiom of Choice

✍ Scribed by B. Germansky

Publisher: John Wiley and Sons
Year: 1961
Tongue: English
Weight: 326 KB
Volume: 7
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.19610071110

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📜 SIMILAR VOLUMES

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

Metric spaces and the axiom of choice

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## 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.

RUSSELL'S ALTERNATIVE TO THE AXIOM OF CH

RUSSELL'S ALTERNATIVE TO THE AXIOM OF CHOICE

✍ Norbert Brunner; Paul Howard 📂 Article 📅 1992 🏛 John Wiley and Sons 🌐 English ⚖ 305 KB 👁 1 views

## 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.

Rigid Unary Functions and the Axiom of C

Rigid Unary Functions and the Axiom of Choice

✍ Wolfgang Degen 📂 Article 📅 2001 🏛 John Wiley and Sons 🌐 English ⚖ 168 KB 👁 2 views

We shall investigate certain statements concerning the rigidity of unary functions which have connections with (weak) forms of the axiom of choice.

Bases, spanning sets, and the axiom of c

Bases, spanning sets, and the axiom of choice

✍ Paul Howard 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 171 KB 👁 1 views

## Abstract Two theorems are proved: First that the statement “there exists a field __F__ such that for every vector space over __F__, every generating set contains a basis” implies the axiom of choice. This generalizes theorems of Halpern, Blass, and Keremedis. Secondly, we prove that the assert

The Compactness of 2ℝ and the Axiom of C

The Compactness of 2ℝ and the Axiom of Choice

✍ Kyriakos Keremedis 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 103 KB 👁 1 views

We show that for every well ordered cardinal number m the Tychonoff product 2 m is a compact space without the use of any choice but in Cohen's Second Model 2 R is not compact.