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Wellfoundedness proof with the maximal distinguished set
Toshiyasu Arai
In arXiv:2208.12944 it is shown that an ordinal is an upper bound for the proof-theoretic ordinal of a set theory ${\sf KP}\…
Refinement of proof-theoretic analysis of the lpo due to Buchholz
Toshiyasu Arai
We give a refinement of proof-theoretic analysis of the lpo (lexicographic path order) due to W. Buchholz. This note was written in Feb. 5, 2015 when G. Moser visited Japan.
A constructive proof of a theorem by Ferreira-Zantema
Toshiyasu Arai
This note was written in Jan. 23, 2015 to answer a problem raised by G. Moser, who asked a constructive proof of a theorem by Ferreira-Zantema.
Two remarks on proof theory of first-order arithmetic
Toshiyasu Arai
In this note let us give two remarks on proof-theory of PA. First a derivability relation is introduced to bound witnesses for provable -formulas in PA. Second Paris-Harring…
Mahlo classes for first-order reflections
Toshiyasu Arai
In this note we axiomatize the -consequences in the set theory for -reflecting universes in terms of iterations of -recursively Mahlo operati…
Predicatively unprovable termination of the Ackermannian Goodstein process
Toshiyasu Arai, David Fernández-Duque, Stanley Wainer +1
The classical Goodstein process gives rise to long but finite sequences of natural numbers whose termination is not provable in Peano arithmetic. In this manuscript we consider a v…