Splitting stationary sets from weak forms of Choice
β Scribed by Paul Larson; Saharon Shelah
- Publisher
- John Wiley and Sons
- Year
- 2009
- Tongue
- English
- Weight
- 120 KB
- Volume
- 55
- Category
- Article
- ISSN
- 0044-3050
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
Working in the context of restricted forms of the Axiom of Choice, we consider the problem of splitting the ordinals below Ξ» of cofinality ΞΈ into Ξ» many stationary sets, where ΞΈ < Ξ» are regular cardinals. This is a continuation of [4] (Β© 2009 WILEYβVCH Verlag GmbH & Co. KGaA, Weinheim)
π SIMILAR VOLUMES
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.
## 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