Finite axiomatizability for profinite groups

Andre Nies; Dan Segal; Katrin Tent

Finite axiomatizability for profinite groups

Group Theory 2021-05-25 v5 Logic

Authors: Andre Nies , Dan Segal , Katrin Tent

Abstract

A group is $\textit{finitely axiomatizable}$ (FA) in a class $\mathcal{C}$ if it can be determined up to isomorphism within $\mathcal{C}$ by a sentence in the first-order language of group theory. We show that profinite groups of various kinds are FA in the class of profinite groups. Reasons why certain groups cannot be FA are also discussed.

Keywords

finite group theory group theory set theory

Cite

@article{arxiv.1907.02262,
  title  = {Finite axiomatizability for profinite groups},
  author = {Andre Nies and Dan Segal and Katrin Tent},
  journal= {arXiv preprint arXiv:1907.02262},
  year   = {2021}
}

Comments

Replaces 'Finite axiomatizability for profinite groups I: group theory', adding significant additional material. New version has better proofs of bi-intepretability

Finite axiomatizability for profinite groups

Abstract

Keywords

Cite

Comments

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