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Summer 1997 Syntax and Semantics of the Logic $\mathcal{L}^\lambda_{\omega\omega}$
Carsten Butz
Notre Dame J. Formal Logic 38(3): 374-384 (Summer 1997). DOI: 10.1305/ndjfl/1039700744


In this paper we study the logic $\mathcal{L}^\lambda_{\omega\omega}$, which is first-order logic extended by quantification over functions (but not over relations). We give the syntax of the logic as well as the semantics in Heyting categories with exponentials. Embedding the generic model of a theory into a Grothendieck topos yields completeness of $\mathcal{L}^\lambda_{\omega\omega}$ with respect to models in Grothendieck toposes, which can be sharpened to completeness with respect to Heyting-valued models. The logic $\mathcal{L}^\lambda_{\omega\omega}$ is the strongest for which Heyting-valued completeness is known. Finally, we relate the logic to locally connected geometric morphisms between toposes.


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Carsten Butz. "Syntax and Semantics of the Logic $\mathcal{L}^\lambda_{\omega\omega}$." Notre Dame J. Formal Logic 38 (3) 374 - 384, Summer 1997.


Published: Summer 1997
First available in Project Euclid: 12 December 2002

zbMATH: 0904.03005
MathSciNet: MR1624950
Digital Object Identifier: 10.1305/ndjfl/1039700744

Primary: 03G30
Secondary: 03C75

Rights: Copyright © 1997 University of Notre Dame


Vol.38 • No. 3 • Summer 1997
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