Abstract
AbstractIn 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.
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