Predicate Logics of Constructive Arithmetical Theories

Journal of Symbolic Logic 71 (4):1311 - 1326 (2006)
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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DOI 10.2178/jsl/1164060457
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References found in this work BETA

Faith & Falsity.Albert Visser - 2004 - Annals of Pure and Applied Logic 131 (1):103-131.
Rules and Arithmetics.Albert Visser - 1999 - Notre Dame Journal of Formal Logic 40 (1):116-140.
No Escape From Vardanyan's Theorem.Albert Visser & Maartje de Jonge - 2006 - Archive for Mathematical Logic 45 (5):539-554.

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

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