PP-2014-10: Changing a semantics: opportunism or courage?

PP-2014-10: Andreka, Hajnal and van Benthem, Johan and Bezhanishvili, Nick and Németi, István (2014) Changing a semantics: opportunism or courage? [Report]

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The generalized models for higher-order logics introduced by Leon Henkin, and their multiple offspring over the years, have become a standard tool in many areas of logic. Even so, discussion has persisted about their technical status, and perhaps even their conceptual legitimacy. This paper gives a systematic view of generalized model techniques, discusses what they mean in mathematical and philosophical terms, and presents a few technical themes and results about their role in algebraic representation, calibrating provability, lowering complexity, understanding fixed-point logics, and achieving set-theoretic absoluteness. We also show how thinking about Henkin’s approach to semantics of logical systems in this generality can yield new results, dispelling the impression of adhocness.

Item Type: Report
Report Nr: PP-2014-10
Series Name: Prepublication (PP) Series
Year: 2014
Uncontrolled Keywords: Henkin models; definable predicates; general frames; absoluteness; general models for recursion and computation
Subjects: Computation
Depositing User: Nick Bezhanishvili
Date Deposited: 12 Oct 2016 14:37
Last Modified: 12 Oct 2016 14:37
URI: https://eprints.illc.uva.nl/id/eprint/498

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