- New
-
Topics
- All Categories
- Metaphysics and Epistemology
- Value Theory
- Science, Logic, and Mathematics
- Science, Logic, and Mathematics
- Logic and Philosophy of Logic
- Philosophy of Biology
- Philosophy of Cognitive Science
- Philosophy of Computing and Information
- Philosophy of Mathematics
- Philosophy of Physical Science
- Philosophy of Social Science
- Philosophy of Probability
- General Philosophy of Science
- Philosophy of Science, Misc
- History of Western Philosophy
- Philosophical Traditions
- Philosophy, Misc
- Other Academic Areas
- Journals
- Submit material
- More
Arithmetical Soundness and Completeness for $$\varvec{\Sigma }_{\varvec{2}}$$ Numerations
Studia Logica 106 (6):1181-1196 (2018)
Abstract
We prove that for each recursively axiomatized consistent extension T of Peano Arithmetic and \, there exists a \ numeration \\) of T such that the provability logic of the provability predicate \\) naturally constructed from \\) is exactly \ \rightarrow \Box p\). This settles Sacchetti’s problem affirmatively.Other Versions
No versions found
My notes
Similar books and articles
Arithmetical Completeness Theorem for Modal Logic $$mathsf{}$$.Taishi Kurahashi - 2018 - Studia Logica 106 (2):219-235.
On predicate provability logics and binumerations of fragments of Peano arithmetic.Taishi Kurahashi - 2013 - Archive for Mathematical Logic 52 (7-8):871-880.
Predicate provability logic with non-modalized quantifiers.Giorgie Dzhaparidze - 1991 - Studia Logica 50 (1):149 - 160.
Arithmetical interpretations and Kripke frames of predicate modal logic of provability.Taishi Kurahashi - 2013 - Review of Symbolic Logic 6 (1):1-18.
Proof-theoretic modal PA-Completeness II: The syntactic countermodel.Paolo Gentilini - 1999 - Studia Logica 63 (2):245-268.
On Inclusions Between Quantified Provability Logics.Taishi Kurahashi - 2021 - Studia Logica 110 (1):165-188.
Complete, Recursively Enumerable Relations in Arithmetic.Giovanna D'Agostino & Mario Magnago - 1995 - Mathematical Logic Quarterly 41 (1):65-72.
Embedding logics into product logic.Matthias Baaz, Petr Hájek, David Švejda & Jan Krajíček - 1998 - Studia Logica 61 (1):35-47.
Analytics
Added to PP
2018-02-10
Downloads
38 (#593,075)
6 months
6 (#858,075)
2018-02-10
Downloads
38 (#593,075)
6 months
6 (#858,075)
Historical graph of downloads
Citations of this work
Current Research on Gödel’s Incompleteness Theorems.Yong Cheng - 2021 - Bulletin of Symbolic Logic 27 (2):113-167.
Another look at the second incompleteness theorem.Albert Visser - 2020 - Review of Symbolic Logic 13 (2):269-295.
The absorption law: Or: how to Kreisel a Hilbert–Bernays–Löb.Albert Visser - 2020 - Archive for Mathematical Logic 60 (3-4):441-468.
Variants of Kreisel’s Conjecture on a New Notion of Provability.Paulo Guilherme Santos & Reinhard Kahle - 2021 - Bulletin of Symbolic Logic 27 (4):337-350.
References found in this work
Arithmetization of Metamathematics in a General Setting.Solomon Feferman - 1960 - Journal of Symbolic Logic 31 (2):269-270.
Syntactical Treatments of Modality, with Corollaries on Reflexion Principles and Finite Axiomatizability.Richard Montague - 1963 - Journal of Symbolic Logic 40 (4):600-601.
Provability Interpretations of Modal Logic.Robert M. Solovay - 1981 - Journal of Symbolic Logic 46 (3):661-662.
Four valued semantics and the liar.Albert Visser - 1984 - Journal of Philosophical Logic 13 (2):181 - 212.
PhilPapers logo by Andrea Andrews and Meghan Driscoll.
This site uses cookies and Google Analytics (see our terms & conditions for details regarding the privacy implications). Use of this site is subject to terms & conditions.
All rights reserved by The PhilPapers Foundation
Server: philpapers-web-667477cd97-7qg25 dc2