PP-2015-04: Changing a Semantics: Opportunism or Courage?

PP-2015-04: Andréka, Hajnal and van Benthem, Johan and Bezhanishvili, Nick and Németi, István (2015) 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.

Appeared in M. Manzano et al. eds., "A Henkin Centernary".

Item Type: Report
Report Nr: PP-2015-04
Series Name: Prepublication (PP) Series
Year: 2015
Uncontrolled Keywords: general models, Henkin, second-order logic, algebraic logic, decidable core, fixed-point logic, set theory
Subjects: Logic
Depositing User: Johan van Benthem
Date Deposited: 12 Oct 2016 14:37
Last Modified: 12 Oct 2016 14:37
URI: https://eprints.illc.uva.nl/id/eprint/515

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