Abstract: Abstruct on Eighth International Conference "Kazakh-French Logical Colloquium" which will be held on June 24-28, 2025 in Astana, Kazakhstan. Strong constructibility of prime and saturated models of theory for recursive ordinal S.S. Goncharov, A.M. Petrenko, V.K. Kravtsov, E.I. Khlestova. In the talk, results acquired as a result of investigation into strong construtibility of models on the basis of ordinal constructions[1] will be presented. It was shown that ordinals smaller than ω^ω are strongly constructive on the basis of criteria for strong constructibility of prime models of decidable theories. The basis of this research is the well known paper by A. Tarski, A. Mostowski, and D. Doner[2] \on the decidability of elementary theories of any ordinal. Using this technique and computability theory it was shown that for any recusive ordinal λ it is possible to build a strongly constructive presentation for ordinal ω^ω × Ω^λ . Theorem. Any computable ordinal is strongly constructive and the prime and saturated their models of these theories decidable too. This result can be used for some inductive constructions of models on the basis of ordinals in order to investigate their decidability. The research of E.I Khlestova was conducted with funding from grant № 23-11-00170 of the Russian Science Foundation, https://rscf.ru/project/23-11-00170/ References [1] Y.L. Ershov, S.S. Goncharov Constructive Models. Springer New York, NY, 2012. [2] Doner J. E., Mostowski, A., Tarski, A. The Elementary Theory of Well-Odering—A Metamathematical Study—. in: Logic Colloquium ’77 (A. Macintyre, L. Pacholski, and J. Paris, eds.), Studies in Logic and the Foundations of Mathematics. 1978. V.96. pp.1—54. Goncharov Sergey Savostyanovich, Sobolev Institute of Mathematics, Novosibirsk e-mail: s.s.goncharov@math.nsc.ru Andrey Mihailovich Petrenko, Novosibirsk State University, Novosibirsk e-mail: a.petrenko2@g.nsu.ru Vladimir Konstantinovich Kravtsov, Novosibirsk State University, Novosibirsk e-mail: v.kravtsov@g.nsu.ru Khlestova Elizaveta Ivanovna, Novosibirsk State University, Novosibirsk e-mail: е.khlestova@g.nsu.ru Novosibirsk State University, Novosibirsk

Cite: Goncharov S.S. , Petrenko A.M. , Kravtsov V.K. , Khlestova E.I.
Strong constructibility of prime and saturated models of theory for recursive ordinal
Eighth International Conference "Kazakh-French Logical Colloquium" 24-28 Jun 2025