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Mathematics > Logic

arXiv:1411.7636 (math)
[Submitted on 27 Nov 2014]

Title:Changing a semantics: opportunism or courage?

Authors:H. Andréka, J. F. A. K. van Benthem, N. Bezhanishvili, I. Németi
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Abstract: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. This paper is dedicated to Leon Henkin, a deep logician who has changed the way we all work, while also being an always open, modest, and encouraging colleague and friend.
Comments: 27 pages. To appear in: The life and work of Leon Henkin: Essays on his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and Alonso, E., 2014
Subjects: Logic (math.LO)
MSC classes: 03H05, 03B15, 03Axx, 03C70, 03C95, 03B70, 03B45, 03B10, 06D50, 68Q55, 03C62
Report number: ILLC Prepublication series PP-2014-10
Cite as: arXiv:1411.7636 [math.LO]
  (or arXiv:1411.7636v1 [math.LO] for this version)
  https://doi.org/10.48550/arXiv.1411.7636
Journal reference: In: The life and work of Leon Henkin. Essays on his contributions. Editors: Maria Manzano, Ildiko Sain and Enrique Alonso., Studies in Universal Logic, Springer, 2014, pp.307-337
Related DOI: https://doi.org/10.1007/978-3-319-09719-0_20

Submission history

From: Hajnal Andréka [view email]
[v1] Thu, 27 Nov 2014 16:11:26 UTC (56 KB)
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