No interesting sequential groups

2016/04/29 by Alexander Shibakov, Shibakov, Alexander
Mathematics · #22A16 #FOS: Mathematics #General Topology (math.GN) #math.GN #msc:22A16

paper · pdf · doi:10.48550/arxiv.1604.08868

arxiv created 2016/04/29 · arxiv updated 2016/05/02

Abstract

We prove that it is consistent with ZFC that no sequential topological groups of intermediate sequential orders exist. This shows that the answer to a 1981 question of P.~Nyikos is independent of the standard axioms of set theory. The model constructed also provides consistent answers to several questions of D.~Shakhmatov, S.~Todorčević and Uzcátegui. In particular, we show that it is consistent with ZFC that every countably compact sequential group is Fréchet-Urysohn.

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• Countably compact groups and sequential order
• Convergence in topological groups and the Cohen reals
• On sequential analytic groups
• On large sequential groups
• Precompact groups and convergence