Permutation models and topological groups
type: Item
instance of: scholarly article
title: Permutation models and topological groups
zbMATH Open document ID: 0622.03037
author: Norbert Brunner
author: Jean E. Rubin
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1986-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108036
review text: Fraenkel-Mostowski models are the classical device for proving independence results for the axiom of choice (AC) in set theory with atoms. In these models the validity of various forms of AC is characterized in terms of the topological automorphism group. Thus a permutation model satisfies Levy's multiple choice axiom (MC), if and only if its group of \(\in\)-automorphisms is locally compact. This implies that in all permutation models MC together with the countable axiom of choice is equivalent to AC. Particular emphasis rests on the investigation of models with a proper class of atoms.
Mathematics Subject Classification ID: 03E25
Mathematics Subject Classification ID: 22D05
zbMATH DE Number: 4008390
zbMATH Keywords: Fraenkel-Mostowski permutation models
zbMATH Keywords: axiom of choice
zbMATH Keywords: topological automorphism group
zbMATH Keywords: multiple choice axiom
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4008390