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August 2021 Generalizing Montague’s Theorem on Recursive Definitions
Edoardo Rivello
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Notre Dame J. Formal Logic 62(3): 553-575 (August 2021). DOI: 10.1215/00294527-2021-0027

Abstract

I study several kinds of generalizations of Montague’s theorem on the method of definition of a function by recursion on a well-founded relation. In particular, I extend Montague’s theorem to cover the following situations: recursion by a valuation system, non-well-founded recursion, and recursion on a dependence operator. By means of these extensions, several constructions employed in formal theories of truth and paradox can be recast as special applications of the generalized version of Montague’s theorem.

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Edoardo Rivello. "Generalizing Montague’s Theorem on Recursive Definitions." Notre Dame J. Formal Logic 62 (3) 553 - 575, August 2021. https://doi.org/10.1215/00294527-2021-0027

Information

Received: 17 July 2019; Accepted: 6 April 2021; Published: August 2021
First available in Project Euclid: 6 October 2021

Digital Object Identifier: 10.1215/00294527-2021-0027

Subjects:
Primary: 03E47
Secondary: 03A10, 03E75

Rights: Copyright © 2021 University of Notre Dame

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Vol.62 • No. 3 • August 2021
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