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Uniqueness of normal proofs of minimal formulas

Published online by Cambridge University Press:  12 March 2014

Makoto Tatsuta
Makoto Tatsuta*
Affiliation:
Research Institute of Electrical Communication, Tohoku University, 2-1-1 Katahira, Sendai 980, Japan, E-mail: tatsuta@riec.tohoku.ac.jp
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Abstract

A minimal formula is a formula which is minimal in provable formulas with respect to the substitution relation. This paper shows the following: (1) A β-normal proof of a minimal formula of depth 2 is unique in NJ. (2) There exists a minimal formula of depth 3 whose βη-normal proof is not unique in NJ. (3) There exists a minimal formula of depth 3 whose βη-normal proof is not unique in NK.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 58 , Issue 3 , September 1993 , pp. 789 - 799
Copyright
Copyright © Association for Symbolic Logic 1993

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References

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