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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2022, Volume 505, Pages 5–10
DOI: https://doi.org/10.31857/S2686954322040038 (Mi danma268) 		 
MATHEMATICS

Conservativity spectra and Joosten–Fernández model

L. D. Beklemishev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
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DOI: https://doi.org/10.31857/S2686954322040038
Abstract: We study a generalization of the notion of conservativity spectrum of an arithmetical theory to a language with transfinitely many truth definitions. We establish a natural correspondence of conservativity spectra and points of a special Kripke model introduced and studied by D. Fernández–Duque and J. Joosten. For iterated reflection principles over theories of truth definitions we also establish conservation results analogous to the well-known Schmerl formulas.
Keywords: reflection principle, truth definition, conservativity.
Funding agency Grant number
Russian Science Foundation 21-11-00318
This work was supported by the Russian Science Foundation under grant no. 21-11-00318, https://rscf.ru/en/project/21-11-00318/.
Received: 24.03.2022
Revised: 05.06.2022
Accepted: 07.06.2022
English version:
Doklady Mathematics, 2022, Volume 106, Issue 1, Pages 213–217
DOI: https://doi.org/10.1134/S1064562422040032
Bibliographic databases:
Document Type: Article
UDC: 510.64
Language: Russian
Citation: L. D. Beklemishev, “Conservativity spectra and Joosten–Fernández model”, Dokl. RAN. Math. Inf. Proc. Upr., 505 (2022), 5–10; Dokl. Math., 106:1 (2022), 213–217
Citation in format AMSBIB
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\by L.~D.~Beklemishev
\paper Conservativity spectra and Joosten--Fern\'andez model
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2022
\vol 505
\pages 5--10
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\crossref{https://doi.org/10.31857/S2686954322040038}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4489401}
\elib{https://elibrary.ru/item.asp?id=49344488}
\transl
\jour Dokl. Math.
\yr 2022
\vol 106
\issue 1
\pages 213--217
\crossref{https://doi.org/10.1134/S1064562422040032}
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