The Closed Fragment of the Interpretability Logic of PRA with a Constant for $\mathrm{I}\Sigma_1$

Notre Dame Journal of Formal Logic 46 (2):127-146 (2005)
  Copy   BIBTEX

Abstract

In this paper we carry out a comparative study of $\mathrm{I}\Sigma_1$ and PRA. We will in a sense fully determine what these theories have to say about each other in terms of provability and interpretability. Our study will result in two arithmetically complete modal logics with simple universal models

Categories

Keywords

Reprint years

DOI

10.1305/ndjfl/1117755145

Other Versions

No versions found

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 107,650

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Provability and Interpretability Logics with Restricted Realizations.Thomas F. Icard & Joost J. Joosten - 2012 - Notre Dame Journal of Formal Logic 53 (2):133-154.
Interpolation and the Interpretability Logic of PA.Evan Goris - 2006 - Notre Dame Journal of Formal Logic 47 (2):179-195.
Preservativity logic: An analogue of interpretability logic for constructive theories.Rosalie Iemhoff - 2003 - Mathematical Logic Quarterly 49 (3):230-249.
An Inside View of Exp; or, The Closed Fragment of the Provability Logic of IΔ0+ Ω1 with a Propositional Constant for.Albert Visser - 1992 - Journal of Symbolic Logic 57 (1):131-165.
A note on the interpretability logic of finitely axiomatized theories.Maarten Rijke - 1991 - Studia Logica 50 (2):241 - 250.
A note on the interpretability logic of finitely axiomatized theories.Maarten de Rijke - 1991 - Studia Logica 50 (2):241-250.
Two new series of principles in the interpretability logic of all reasonable arithmetical theories.Evan Goris & Joost J. Joosten - 2020 - Journal of Symbolic Logic 85 (1):1-25.
Bisimulations between generalized Veltman models and Veltman models.Mladen Vuković - 2008 - Mathematical Logic Quarterly 54 (4):368-373.
A Note on Bisimulation and Modal Equivalence in Provability Logic and Interpretability Logic.Vedran Čačić & Domagoj Vrgoč - 2013 - Studia Logica 101 (1):31-44.
The provability logic for Σ1-interpolability.Konstantin N. Ignatiev - 1993 - Annals of Pure and Applied Logic 64 (1):1-25.

Analytics

Added to PP
2010-08-24

Downloads
81 (#290,728)

6 months
21 (#172,617)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Joost Joosten
Universitat de Barcelona

Citations of this work

Add more citations

References found in this work

Finitism.W. W. Tait - 1981 - Journal of Philosophy 78 (9):524-546.
Arithmetization of Metamathematics in a General Setting.Solomon Feferman - 1960 - Journal of Symbolic Logic 31 (2):269-270.
The interpretability logic of peano arithmetic.Alessandro Berarducci - 1990 - Journal of Symbolic Logic 55 (3):1059-1089.
On n-quantifier induction.Charles Parsons - 1972 - Journal of Symbolic Logic 37 (3):466-482.

View all 17 references / Add more references