Polish algebras, shy from freedom.

DOI10.1007/s11856-011-0020-xzbMath1233.20001arXivmath/0212250OpenAlexW2020640109MaRDI QIDQ532598

Saharon Shelah

Publication date: 5 May 2011

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0212250

zbMATH Keywords

free groupsPolish groupsfree Abelian groupsautomorphism groups of uncountable structures

Mathematics Subject Classification ID

Structure of general topological groups (22A05) Applications of logic to group theory (20A15) Model-theoretic algebra (03C60) Descriptive set theory (03E15) Topological groups (topological aspects) (54H11) Infinite automorphism groups (20B27)

Related Items (6)

Polish topologies for graph products of cyclic groups ⋮ Beginning of stability theory for Polish spaces ⋮ New metrics on free groups ⋮ A parallel to the null ideal for inaccessible \(\lambda\). I ⋮ No uncountable Polish group can be a right-angled Artin group ⋮ Polish topologies for graph products of groups

Cites Work

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• Beginning of stability theory for Polish spaces
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• Classification theory for non-elementary classes. I: The number of uncountable models of \(\psi \in L_{\omega _ 1,\omega}\)
• Categoricity results for \(L_{\infty \kappa}\)-free algebras
• Classification theory and the number of non-isomorphic models.
• Analytic ideals and their applications
• Almost free algebras
• The automorphism tower problem revisited
• A COUNTABLE STRUCTURE DOES NOT HAVE A FREE UNCOUNTABLE AUTOMORPHISM GROUP

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