Rich groups, weak second-order logic, and applications

Olga Kharlampovich, Alexei Myasnikov, Mahmood Sohrabi

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

5 Scopus citations

Abstract

In this chapter we initiate a study of first-order rich groups, i. e., groups where the first-order logic has the same power as the weak second-order logic. Surprisingly, there are quite a few finitely generated rich groups, they are somewhere inbetween hyperbolic and nilpotent groups (these are not rich). We provide some methods to prove that groups (and other structures) are rich and describe some of their properties. As corollaries we look at Malcev's problems in various groups.

Original languageEnglish
Title of host publicationGroups and Model Theory
Subtitle of host publicationGAGTA BOOK 2
Pages127-191
Number of pages65
ISBN (Electronic)9783110719710
DOIs
StatePublished - 24 May 2021

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