Almost free groups and Ehrenfeucht-Fraïssé games for successors of singular cardinals

Saharon Shelah; Pauli Väisänen

doi:10.1016/S0168-0072(02)00037-4

Almost free groups and Ehrenfeucht-Fraïssé games for successors of singular cardinals

Saharon Shelah, Pauli Väisänen^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We strengthen nonstructure theorems for almost free Abelian groups by studying long Ehrenfeucht-Fraïssé games between a fixed group of cardinality λ and a free Abelian group. A group is called ε-game-free if the isomorphism player has a winning strategy in the game (of the described form) of length ε ∈ λ. We prove for a large set of successor cardinals λ = μ⁺ the existence of nonfree (μ · ω₁)-game-free groups of cardinality λ. We concentrate on successors of singular cardinals.

Original language	English
Pages (from-to)	147-173
Number of pages	27
Journal	Annals of Pure and Applied Logic
Volume	118
Issue number	1-2
DOIs	https://doi.org/10.1016/S0168-0072(02)00037-4
State	Published - 1 Dec 2002

Keywords

Almost free groups
Ehrenfeucht-Fraíssé games

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10.1016/S0168-0072(02)00037-4

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AU - Väisänen, Pauli

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N2 - We strengthen nonstructure theorems for almost free Abelian groups by studying long Ehrenfeucht-Fraïssé games between a fixed group of cardinality λ and a free Abelian group. A group is called ε-game-free if the isomorphism player has a winning strategy in the game (of the described form) of length ε ∈ λ. We prove for a large set of successor cardinals λ = μ+ the existence of nonfree (μ · ω1)-game-free groups of cardinality λ. We concentrate on successors of singular cardinals.

AB - We strengthen nonstructure theorems for almost free Abelian groups by studying long Ehrenfeucht-Fraïssé games between a fixed group of cardinality λ and a free Abelian group. A group is called ε-game-free if the isomorphism player has a winning strategy in the game (of the described form) of length ε ∈ λ. We prove for a large set of successor cardinals λ = μ+ the existence of nonfree (μ · ω1)-game-free groups of cardinality λ. We concentrate on successors of singular cardinals.

KW - Almost free groups

KW - Ehrenfeucht-Fraíssé games

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Almost free groups and Ehrenfeucht-Fraïssé games for successors of singular cardinals

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