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Logic Colloquium 2024

Speaker

Nurlan Markhabatov

L.N. Gumilyov Eurasian National University

Talks at this conference:

  Tuesday, 16:30, J330

On Disintegrated Models

Definition 1. [1] Let T be a family of theories and T be a theory such that TT. The theory T is said to be T-approximated, or approximated by the family T, or a pseudo-T-theory, if for any formula φT there exists TT for which φT.

Definition 2. An infinite model M of a T-approximated theory T is called disintegrated if it is a disjoint union of models, M=iωMi, where Mi is finite (possibly either ω-categorical or minimal). Otherwise, M is called integrated.

Theorem. Any disintegrated infinite model is pseudofinite.

Theorem. There is an integrated model, which is pseudofinite.

This research was funded by the Science Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan (Grant No. AP19677451, AP22782938).

Bibliography

  1. S.V. Sudoplatov, Approximations of theories, Siberian Electronic Mathematical Reports, 17, (2020), pp. 715–725. https://doi.org/10.33048/semi.2020.17.049

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