Properties of the real line and weak forms of the Axiom of Choice
β Scribed by Omar De la Cruz; Eric Hall; Paul Howard; Kyriakos Keremedis; Eleftherios Tachtsis
- Publisher
- John Wiley and Sons
- Year
- 2005
- Tongue
- English
- Weight
- 192 KB
- Volume
- 51
- Category
- Article
- ISSN
- 0044-3050
No coin nor oath required. For personal study only.
β¦ Synopsis
Axiom of Choice, weak axioms of choice, real line.
MSC (2000) 03E25, 03E35
We investigate, within the framework of Zermelo-Fraenkel set theory ZF, the interrelations between weak forms of the Axiom of Choice AC restricted to sets of reals.
π SIMILAR VOLUMES
## Abstract A weak form of intuitionistic set theory **WST** lacking the axiom of extensionality is introduced. While **WST** is too weak to support the derivation of the law of excluded middle from the axiom of choice, we show that bee.ng up **WST** with moderate extensionality principles or quoti
## Abstract We study statements about countable and wellβordered unions and their relation to each other and to countable and wellβordered forms of the axiom of choice. Using WO as an abbreviation for βwellβorderableβ, here are two typical results: The assertion that every WO family of countable se