On a Strengthening of the Non-Isomorphism Theorem for Provability Algebras

We prove a strengthened version of V. Shavrukov’s result on the non-isomorphism of provability algebras of two Σ 1 -sound theories, based on the improvements previously discovered by G. Adamsson. We then obtain several corollaries to the strengthened result by applying it to various pairs of theorie...

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Bibliographic Details
Published inDoklady. Mathematics Vol. 104; no. 1; pp. 180 - 183
Main Author Kolmakov, E. A.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.07.2021
Springer Nature B.V
Subjects
Isomorphism
Mathematics
Mathematics and Statistics
reflection principle
provability predicate
provability algebra
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Summary:We prove a strengthened version of V. Shavrukov’s result on the non-isomorphism of provability algebras of two Σ 1 -sound theories, based on the improvements previously discovered by G. Adamsson. We then obtain several corollaries to the strengthened result by applying it to various pairs of theories and obtain new non-isomorphism examples. In particular, we show that there are no epimorphisms from onto .
ISSN:1064-5624
1531-8362
DOI:10.1134/S1064562421040086