Finite axiomatizability for profinite groups

2019/07/04 by Nies, Andre, Segal, Dan, Tent, Katrin · 1 citation
#20A15 #20E18 #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO)

paper · doi:10.48550/arxiv.1907.02262

Abstract

A group is finitely axiomatizable (FA) in a class C if it can be determined up to isomorphism within 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.

Cited by

• Open Problems in Computability Theory and Descriptive Set Theory

Related

• On the finite axiomatizability of some metabelian profinite groups
• Finiteness properties of profinite groups
• A profinite analogue of Lasserre's theorem
• Property FA is not a profinite property
• Some aspects of profinite group theory