Canonical universal locally finite groups

Saharon Shelah

doi:10.4171/RSMUP/117

Canonical universal locally finite groups

Saharon Shelah^*

^*Corresponding author for this work

Einstein Institute of Mathematics

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

Abstract

We prove that the existence of universally locally finite groups implies that there is a canonical one in any strong limit singular cardinality of countable cofinality. Moreover, those canonical groups are parallel to the special models for complete first order theories. For showing the existence we rely on the existence of enough indecomposable such groups as we proved in [Rend. Sem. Mat. Univ. Padova 144 (2020), 253–270]. More generally, we also deal with the existence of a universal member in general classes for such cardinals.

Original language	English
Pages (from-to)	25-44
Number of pages	20
Journal	Rendiconti del Seminario Matematico dell 'Universita' di Padova/Mathematical Journal of the University of Padova
Volume	149
DOIs	https://doi.org/10.4171/RSMUP/117
State	Published - 2023

Bibliographical note

Publisher Copyright:
© 2023 Università degli Studi di Padova Published by EMS Press.

Keywords

applications of model theory
canonical groups
groups
indecomposable groups
locally finite groups
Model theory

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10.4171/RSMUP/117

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abstract = "We prove that the existence of universally locally finite groups implies that there is a canonical one in any strong limit singular cardinality of countable cofinality. Moreover, those canonical groups are parallel to the special models for complete first order theories. For showing the existence we rely on the existence of enough indecomposable such groups as we proved in [Rend. Sem. Mat. Univ. Padova 144 (2020), 253–270]. More generally, we also deal with the existence of a universal member in general classes for such cardinals.",

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ER -

Canonical universal locally finite groups

Abstract

Bibliographical note

Keywords

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