REFLECTION RANKS AND ORDINAL ANALYSIS

Autor: Fedor Pakhomov, James Walsh

Publikováno v: Walsh, James; & Pakhomov, Fedor. (2018). Reflection ranks and ordinal analysis. UC Berkeley: Group in Logic and the Methodology of Science. Retrieved from: http://www.escholarship.org/uc/item/1159j6ck
JOURNAL OF SYMBOLIC LOGIC

It is well-known that natural axiomatic theories are well-ordered by consistency strength. However, it is possible to construct descending chains of artificial theories with respect to consistency strength. We provide an explanation of this well-orde

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::65d30654d203cc4a7c959653aabe77b6
https://doi.org/10.1017/jsl.2020.9

Reducing $ω$-model reflection to iterated syntactic reflection

Autor: James Walsh, Fedor Pakhomov

In mathematical logic there are two seemingly distinct kinds of principles called "reflection principles." Semantic reflection principles assert that if a formula holds in the whole universe, then it holds in a set-sized model. Syntactic reflection p

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8f80e414b2fda6a14406b2fc77ce24c0

Truth, disjunction, and induction

Autor: Ali Enayat, Fedor Pakhomov

Publikováno v: ARCHIVE FOR MATHEMATICAL LOGIC

By a well-known result of Kotlarski, Krajewski, and Lachlan (1981), first-order Peano arithmetic $PA$ can be conservatively extended to the theory $CT^{-}[PA]$ of a truth predicate satisfying compositional axioms, i.e., axioms stating that the truth

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::27dfb64c57d1116591c68787049a5d1b
https://hdl.handle.net/1854/LU-8735654

Interpretations of Presburger Arithmetic in Itself

Autor: Alexander Zapryagaev, Fedor Pakhomov

Publikováno v: Logical Foundations of Computer Science ISBN: 9783319720555
LFCS

Presburger arithmetic \(\mathop {\mathbf {PrA}}\nolimits \) is the true theory of natural numbers with addition. We study interpretations of \(\mathop {\mathbf {PrA}}\nolimits \) in itself. We prove that all one-dimensional self-interpretations are d

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::1adac23bf5b696db66601aac56efe8c1
https://doi.org/10.1007/978-3-319-72056-2_22

On the complexity of the closed fragment of Japaridze’s provability logic

Autor: Fedor Pakhomov

Publikováno v: Archive for Mathematical Logic. 53:949-967

We consider the well-known provability logic GLP. We prove that the GLP-provability problem for polymodal formulas without variables is PSPACE-complete. For a number n, let $${L^{n}_0}$$ L 0 n denote the class of all polymodal variable-free formulas

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::94c861ab4aaa10c4a1981e6838cf937d
https://doi.org/10.1007/s00153-014-0397-4