Amb motiu del tancament d'estiu, la validació de documents es reprendrà a partir del 28 d'agost de 2026. Disculpeu les molèsties.
Con motivo del cierre de verano, la validación de documentos se reanudará a partir del 28 de agosto de 2026. Disculpad las molestias
Due to the summer closure, document validation will resume starting August 28, 2026. We apologize for any inconvenience.

Files

250435.pdf (303.51 KB)

Document type

Article

Version

Published version

Publication date

2023

Publication license

cc-by (c) Borges, Ana de Almeida Gabriel Vieira et al, 2023
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/217429

An Escape from Vardanyan's Theorem

Journal Title

Authors

Director/Tutor

Journal ISSN

Volume Title

Related resource

https://doi.org/10.1017/jsl.2022.38

Abstract

Vardanyan’s Theorems [36, 37] state that QPL(PA)—the quantified provability logic of Peano Arithmetic—isΠ02 complete, and in particular that this already holds when the language is restricted to a single unary predicate. Moreover, Visser and de Jonge [38] generalized this result to conclude that it is impossible to computably axiomatize the quantified provability logic of a wide class of theories. However, the proof of this fact cannot be performed in a strictly positive signature. The system QRC1 was previously introduced by the authors [1] as a candidate first-order provability logic. Here we generalize the previously available Kripke soundness and completeness proofs, obtaining constant domain completeness. Then we show that QRC1 is indeed complete with respect to arithmetical semantics. This is achieved via a Solovaytype construction applied to constant domain Kripke models. As corollaries, we see that QRC1 is the strictly positive fragment of QGL and a fragment of QPL(PA).

Subject

Modalitat (Lògica), Aritmètica, Lògica matemàtica

Subject (English)

Modality (Logic), Arithmetic, Mathematical logic

Citation

Collections

Articles publicats en revistes (Filosofia)

Citation

BORGES, Ana de Almeida Gabriel Vieira and JOOSTEN, Joost J. An Escape from Vardanyan's Theorem. Journal of Symbolic Logic. 2023. Vol. 88, num. 4, pags. 1613-1638. ISSN 0022-4812. [consulted: 19 of August of 2026]. Available at: https://hdl.handle.net/2445/217429

Export metadata

JSON - METS

Share record