24 August 2021
Proceedings of the London Mathematical Society
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, or in the class of pro- 𝑝 groups for some prime 𝑝 . Both algebraic and model-theoretic methods are developed for the purpose. Reasons why certain groups cannot be FA are also discussed.
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