Positive Frege and its Scott‐style semantics

Mathematical Logic Quarterly 54 (4):410-434 (2008)
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Abstract

We show that the untyped λ -calculus can be extended with Frege's interpretation of propositional notions, provided we restrict β -conversion to positive expressions. The system of illative λ -calculus so obtained admits a natural Scott-style semantics

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10.1002/malq.200710053

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Citations of this work

The universal set and diagonalization in Frege structures.Reinhard Kahle - 2011 - Review of Symbolic Logic 4 (2):205-218.

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References found in this work

Positive abstraction and extensionality.Roland Hinnion & Thierry Libert - 2003 - Journal of Symbolic Logic 68 (3):828-836.
On the consistency of the first-order portion of Frege's logical system.Terence Parsons - 1987 - Notre Dame Journal of Formal Logic 28 (1):161-168.
Implication and analysis in classical frege structures.Robert C. Flagg & John Myhill - 1987 - Annals of Pure and Applied Logic 34 (1):33-85.
A type-free system extending.John Myhill & Bob Flagg - 1989 - Annals of Pure and Applied Logic 43 (1):79-97.

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