The Principles of Interpretability

Mladen Vuković

Source: Notre Dame J. Formal Logic Volume 40, Number 2 (1999), 227-235.

Abstract

A generalized Veltman semantics developed by de Jongh is used to investigate correspondences between several extensions of intepretability logic $\mathit{IL}$ . In this paper we present some new results on independences.

Primary Subjects: 03B45

Secondary Subjects: 03F40

Full-text: Open access

Screen Optimized PDF File (80 KB)
PDF File (59 KB)

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1038949538
Mathematical Reviews number (MathSciNet): MR1816890
Digital Object Identifier: doi:10.1305/ndjfl/1038949538
Zentralblatt MATH identifier: 0972.03059

back to Table of Contents

References

[1] de Jongh, D., and F. Veltman, ``Provability logics for relative interpretability,'' pp. 31--42 in Mathematical Logic, Proceedings of the 1988 Heyting Conference, edited by P. P. Petkov, Plenum Press, New York, 1990.

Mathematical Reviews (MathSciNet): MR92d:03011

Zentralblatt MATH: 0794.03026

[2] Hájek, P., ``Interpretability in theories containing arithmetic II,'' Commentationes Mathematicae Universitatis Carolinae, vol. 22 (1981), pp. 667--88.

Mathematical Reviews (MathSciNet): MR83j:03094

Zentralblatt MATH: 0487.03032

[3] Solovay, R. M., ``Provability interpretations of modal logic,'' Israel Journal of Mathematics, vol. 25 (1976), pp. 287--304.

Mathematical Reviews (MathSciNet): MR56:15369

Zentralblatt MATH: 0352.02019

Digital Object Identifier: doi:10.1007/BF02757006

[4] Švejdar, V., ``Modal analysis of generalized Rosser sentences,'' The Journal of Symbolic Logic, vol. 48 (1983), pp. 986--99.

Mathematical Reviews (MathSciNet): MR85k:03041

Zentralblatt MATH: 0543.03010

JSTOR: links.jstor.org

Digital Object Identifier: doi:10.2307/2273663

[5] Švejdar, V., ``Some independence results in interpretability logic,'' Studia Logica, vol. 50 (1991), pp. 29--38.

Mathematical Reviews (MathSciNet): MR93c:03026

Zentralblatt MATH: 0728.03016

Digital Object Identifier: doi:10.1007/BF00370385

[6] Visser, A., ``Interpretability logic,'' pp. 175--210 in Mathematical Logic, Proceedings of the 1988 Heyting Conference, edited by P. P. Petkov, Plenum Press, New York, 1990.

Mathematical Reviews (MathSciNet): MR93k:03022

Zentralblatt MATH: 0793.03064

[7] Visser, A., ``The formalization of interpretability,'' Studia Logica, vol. 50 (1991), pp. 81--105.

Mathematical Reviews (MathSciNet): MR93f:03009

Zentralblatt MATH: 0744.03023

Digital Object Identifier: doi:10.1007/BF00370389

[8] Visser, A., ``An overview of interpretability,'' pp. 307--59 in Advances in Modal Logic, edited by M. Kracht, M. de Rijke, and H. Wansing, CSLI Publications, Stanford, 1996.

Mathematical Reviews (MathSciNet): MR1688529

Zentralblatt MATH: 0915.03020

[9] Vuković, M., ``Some correspondences of principles in interpretability logic,'' Glasnik Matematički, vol. 31 (1996), pp. 193--200.

Mathematical Reviews (MathSciNet): MR98i:03076

Zentralblatt MATH: 0871.03043

[10] Vuković, M., ``Interpretability logic and generalized Veltman models,'' abstract, The Bulletin of Symbolic Logic, vol. 6 (2000), p. 131.

[11] Vuković, M., ``Characteristic classes and bisimulations of generalized Veltman models,'' Grazer Mathematische Berichte, vol. 341 (1999), pp. 7--16.

Mathematical Reviews (MathSciNet): MR1816205

Zentralblatt MATH: 01606606

previous :: next