activity
19982023
most citedIterating the recursively Mahlo operations

9 citations · 38 across the 43 of their papers we have counts for

collaborators

44 papers

math.LO2023

An ordinal analysis of -Collection

Toshiyasu Arai

In this paper we give an ordinal analysis of a set theory with -Collection.

math.LO2023

Well-foundedness proof for -reflection

Toshiyasu Arai

In the lecture notes it is shown that an ordinal is an upper bound for the proof-theoretic ordinal of a set theory ${\sf KP}ω+(M\prec_{Σ_{1}}V…

math.LO2023

Lectures on Ordinal Analysis

Toshiyasu Arai

This is a lecture notes for a mini-course in Department of Mathematics, Ghent University, 14 Mar.-25 Mar. 2023.

math.LO2023

Provably well-founded strict partial orders

Toshiyasu Arai

In this note we show through infinitary derivations that each provably well-founded strict partial order in admits an embedding to an ordinal.

math.LO2022

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}\…

math.LO2022

An ordinal analysis of a single stable ordinal

Toshiyasu Arai

In this paper we give an ordinal analysis of a set theory extending with an axiom stating that `there exists a transitive set such that '.