Predicate Logics of Constructive Arithmetical Theories

Journal of Symbolic Logic 71 (4):1311 - 1326 (2006)
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Abstract

In this paper, we show that the predicate logics of consistent extensions of Heyting's Arithmetic plus Church's Thesis with uniqueness condition are complete $\Pi _{2}^{0}$. Similarly, we show that the predicate logic of HA*, i.e. Heyting's Arithmetic plus the Completeness Principle (for HA*) is complete $\Pi _{2}^{0}$. These results extend the known results due to Valery Plisko. To prove the results we adapt Plisko's method to use Tennenbaum's Theorem to prove 'categoricity of interpretations' under certain assumptions

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Citations of this work

Reply to Crispin Wright and Richard Zach.Ian Rumfitt - 2018 - Philosophical Studies 175 (8):2091-2103.

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References found in this work

The Logic of Provability.Philip Scowcroft - 1995 - Philosophical Review 104 (4):627.
The predicate modal logic of provability.Franco Montagna - 1984 - Notre Dame Journal of Formal Logic 25 (2):179-189.
Faith & falsity.Albert Visser - 2004 - Annals of Pure and Applied Logic 131 (1-3):103-131.
Rules and Arithmetics.Albert Visser - 1999 - Notre Dame Journal of Formal Logic 40 (1):116-140.

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