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Predicate Logics of Constructive Arithmetical Theories

Published online by Cambridge University Press:  12 March 2014

Albert Visser
Albert Visser*
Affiliation:
Department of Philosophy, Utrecht University, Heidelberglaan 8, 3584 CS Utrecht, The Netherlands, E-mail: Albert.Visser@phil.uu.nl
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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 . 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.

Keywords

Relative interpretationspredicate logics of arithmetical theoriesconstructive logic
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 71 , Issue 4 , December 2006 , pp. 1311 - 1326
Copyright
Copyright © Association for Symbolic Logic 2006

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References

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