Weihrauch Complexity for Elementary Embeddings into Countable Saturated Models Full article
| Journal |
Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260 |
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| Output data | Year: 2026, Volume: 67, Number: 3, Pages: 701-715 Pages count : 15 DOI: 10.1134/s0037446626030134 | ||
| Tags | Weihrauch reducibility, elementary embedding, countable saturated model | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Министерство науки и высшего образования РФ | FWNF-2026-0032 |
Abstract:
Foraclass of models K, westudythe Weihrauch complexity of the following model-theoretic problem: finding an elementary embedding of an arbitrary model M∈Kinto a countable saturated model N such that N∈Kand N is elementarily equivalent to M. We prove that for the classes of linear orders, Boolean algebras, and abelian groups, this problem is strongly Weihrauch equivalent to the problem lim (that is, the problem of computing the limit in Baire space). We isolate some natural classes K consisting of equivalence structures such that the corresponding problem for K has Weihrauch degree strictly less than the degree of lim.
Cite:
Bazhenov N.A.
, Marchuk M.I.
Weihrauch Complexity for Elementary Embeddings into Countable Saturated Models
Siberian Mathematical Journal. 2026. V.67. N3. P.701-715. DOI: 10.1134/s0037446626030134 WOS Scopus РИНЦ OpenAlex
Weihrauch Complexity for Elementary Embeddings into Countable Saturated Models
Siberian Mathematical Journal. 2026. V.67. N3. P.701-715. DOI: 10.1134/s0037446626030134 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Jul 18, 2025 |
| Accepted: | Jan 1, 2026 |
| Published print: | Jun 25, 2026 |
| Published online: | Jun 25, 2026 |
Identifiers:
| ≡ Web of science: | WOS:001805258500012 |
| ≡ Scopus: | 2-s2.0-105042956967 |
| ≡ Elibrary: | 91538056 |
| ≡ OpenAlex: | W7165893369 |