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Preprint Number 2082
2082. Márton Elekes, Boglárka Gehér, Kristóf Kanalas, Tamás Kátay, Tamás Keleti
Generic countably infinite groups
Submission date: 29 October 2021
Abstract: We have very recently become aware of the fact that another research group is working on very similar problems, see arXiv:2006.14048.
Countably infinite groups (with a fixed underlying set) constitute a Polish
space G with a suitable metric, hence the Baire category theorem holds in
G. We study isomorphism invariant subsets of G, which we call group
properties. We say that the generic countably infinite group is of property P
if P is comeager in G.
Mathematics Subject Classification:
Keywords and phrases:
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