On characterization, definability and ω-saturated models

Authors:
Facundo Carreiro
Affiliations:
Dto. de Computación, FCEyN, Universidad de Buenos Aires
Venue:
ICTAC'11 Proceedings of the 8th international conference on Theoretical aspects of computing
Year:
2011

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Abstract

Two important classic results about modal expressivity are the Characterization and Definability theorems. We develop a general theory for modal logics below first order (in terms of expressivity) which exposes the following result: Characterization and Definability theorems hold for every (reasonable) modal logic whose ω-saturated models have the Hennessy-Milner property. The results are presented in a general version which is relativized to classes of models.