Interpolation and Preservation in ${\cal M\kern-1pt L}{\omega1}$

Notre Dame Journal of Formal Logic 39 (2):190-211 (1998)
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Abstract

In this paper we deal with the logic ${\cal M\kern-1pt L}_{\omega_1}$ which is the infinitary extension of propositional modal logic that has conjunctions and disjunctions only for countable sets of formulas. After introducing some basic concepts and tools from modal logic, we modify Makkai's generalization of the notion of consistency property to make it fit for modal purposes. Using this construction as a universal instrument, we prove, among other things, interpolation for ${\cal M\kern-1pt L}_{\omega_1}$ as well as preservation results for universal, existential, and positive ${\cal M\kern-1pt L}_{\omega_1}$-formulas

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References found in this work

Generalized quantifiers and modal logic.Wiebe Van Der Hoek & Maarten De Rijke - 1993 - Journal of Logic, Language and Information 2 (1):19-58.
Interpolation, Preservation, and Pebble Games.Jon Barwise & Johan van Benthem - 1999 - Journal of Symbolic Logic 64 (2):881 - 903.
Logic of transition systems.Johan Van Benthem & Jan Bergstra - 1994 - Journal of Logic, Language and Information 3 (4):247-283.
Generalized quantifiers and modal logic.Wiebe Hoek & Maarten Rijke - 1993 - Journal of Logic, Language and Information 2 (1):19-58.

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