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.
Citation
Holger Sturm. "Interpolation and Preservation in ${\cal M\kern-1pt L}_{\omega_1}$." Notre Dame J. Formal Logic 39 (2) 190 - 211, Spring 1998. https://doi.org/10.1305/ndjfl/1039293062
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