Submission date: 17 August 2021

Abstract:

We find new “reasons” for a class of models for not having a universal model in a cardinal λ. This work, though has consequences in model theory, is really in combinatorial (set theory). We concentrate on a prototypical class which is a simply defined class of models, of combinatorial character - models of T_{ceq} (essentially another representation of T_{feq} which was already considered but the proof with T_{ceq} is more transparent). Models of T_{ceq} consist essentially of an equivalence relation on one set and a family of choice functions for it. This class is not simple (in the model theoretic sense) but seems to be very low among the non-simple (first order complete countable) ones. We give sufficient conditions for the non-existence of a universal model for it in λ. This work is continued in [Sh:F2071].

Mathematics Subject Classification: 03E05, 03E45

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Full text arXiv 2108.06727: pdf, ps.