# Sh:1164

- Shelah, S. (2023).
*Universality: new criterion for non-existence*. Boll. Unione Mat. Ital.,**16**(1), 43–64. arXiv: 2108.06727 DOI: 10.1007/s40574-022-00327-7 MR: 4548558 -
Abstract:

We find new “reasons" for a class of models for not having a universal model in a cardinal \lambda. 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_{\rm ceq} (essentially another representation of T_{\rm feq} which was already considered but the proof with T_{\rm ceq} is more transparent). Models of T_{\rm 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 \lambda. This work is continued in [Sh:F2071]. - Version 2022-07-19_2 (25p) published version (22p)

Bib entry

@article{Sh:1164, author = {Shelah, Saharon}, title = {{Universality: new criterion for non-existence}}, journal = {Boll. Unione Mat. Ital.}, fjournal = {Bollettino dell'Unione Matematica Italiana}, volume = {16}, number = {1}, year = {2023}, pages = {43--64}, issn = {1972-6724}, mrnumber = {4548558}, mrclass = {03E05 (03C45 03C50 03C55)}, doi = {10.1007/s40574-022-00327-7}, note = {\href{https://arxiv.org/abs/2108.06727}{arXiv: 2108.06727}}, arxiv_number = {2108.06727} }