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Predicate Logics of Constructive Arithmetical Theories
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- Journal:
- The Journal of Symbolic Logic / Volume 71 / Issue 4 / December 2006
- Published online by Cambridge University Press:
- 12 March 2014, pp. 1311-1326
- Print publication:
- December 2006
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- Article
- Export citation
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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
. Similarly, we show that the predicate logic of HA*. i.e. Heyting's Arithmetic plus the Completeness Principle (for HA*) is complete . 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.
. Similarly, we show that the predicate logic of HA*. i.e. Heyting's Arithmetic plus the Completeness Principle (for HA*) is complete 