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)

@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}
}