Two new series of principles in the interpretability logic of all reasonable arithmetical theories

Journal of Symbolic Logic 85 (1):1-25 (2020)
  Copy   BIBTEX

Abstract

The provability logic of a theory T captures the structural behavior of formalized provability in T as provable in T itself. Like provability, one can formalize the notion of relative interpretability giving rise to interpretability logics. Where provability logics are the same for all moderately sound theories of some minimal strength, interpretability logics do show variations.The logic IL is defined as the collection of modal principles that are provable in any moderately sound theory of some minimal strength. In this article we raise the previously known lower bound of IL by exhibiting two series of principles which are shown to be provable in any such theory. Moreover, we compute the collection of frame conditions for both series.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 76,442

External links

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

Through your library

Similar books and articles

Interpretability in.Marta Bílková, Dick de Jongh & Joost J. Joosten - 2010 - Annals of Pure and Applied Logic 161 (2):128-138.
Interpretability Over Peano Arithmetic.Claes Strannegard - 1999 - Journal of Symbolic Logic 64 (4):1407-1425.
Hammond.Claes Strannegard - 1999 - Journal of Symbolic Logic 64 (4):1407-1425.
Interpretability over peano arithmetic.Claes Strannegård - 1999 - Journal of Symbolic Logic 64 (4):1407-1425.
Modal analysis of generalized Rosser sentences.Vítězslav Švejdar - 1983 - Journal of Symbolic Logic 48 (4):986-999.
Modal Matters for Interpretability Logics.Evan Goris & Joost Joosten - 2008 - Logic Journal of the IGPL 16 (4):371-412.
Logicism, Interpretability, and Knowledge of Arithmetic.Sean Walsh - 2014 - Review of Symbolic Logic 7 (1):84-119.
Interpolation and the Interpretability Logic of PA.Evan Goris - 2006 - Notre Dame Journal of Formal Logic 47 (2):179-195.

Analytics

Added to PP
2019-12-13

Downloads
15 (#701,025)

6 months
1 (#454,876)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Joost Joosten
Universitat de Barcelona

References found in this work

No references found.

Add more references