71 search results - page 1 / 15 » Unions and the axiom of choice |
MLQ
2008
13 years 5 months ago
2008
We study statements about countable and well ordered unions and how they are related to each other and to countable and well ordered forms of the axiom of choice.
MLQ
1998
13 years 5 months ago
1998
We find properties of topological spaces which are not shared by disjoint unions in the absence of some form of the Axiom of Choice.
MLQ
1998
13 years 5 months ago
1998
Abstract. We investigate the set theoretical strength of some properties of normality, including Urysohn’s Lemma, Tietze-Urysohn Extension Theorem, normality of disjoint unions o...
AML
2011
13 years 17 days ago
2011
In this paper we prove three theorems about the theory of Borel sets in models of ZF without any form of the axiom of choice. We prove that if B ⊆ 2ω is a Gδσ-set then either...
MLQ
2000
13 years 5 months ago
2000
The axiom of multiple choice implies that metric spaces are paracompact but the reverse implication cannot be proved in set theory without the axiom of choice.