Cut-elimination for $\omega_{1}$
Arai, Toshiyasu;
Cut-elimination for $\omega_{1}$
In this paper we calibrate the strength of the soundness of a Kripke-Platek set theory with the axioms of Infinity and \Pi_{1}-Collection with the assumption that`there exists an uncountable regular ordinal' in terms of the existence of ordinals.
Comment: arXiv admin note: text overlap with arXiv:1508.01548
03F99, uncountable regular ordinal, Structure of proofs, cut-elimination, Cut-elimination and normal-form theorems, Mathematics - Logic, Recursive ordinals and ordinal notations, reflection principle
03F99, uncountable regular ordinal, Structure of proofs, cut-elimination, Cut-elimination and normal-form theorems, Mathematics - Logic, Recursive ordinals and ordinal notations, reflection principle
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