1 citations · 1 across the 3 of their papers we have counts for
3 papers
math.LO2018
Developing Takeuti-Yasumoto forcing
Satoru Kuroda
In late 90's G.Takeuti and Y.Yasumoto gave forcing constructions for bounded arithmetic. We will reformulate their constructions using two-sort bounded arithmetic and prove the fol…
math.LO2016
Sprague-Grundy theory in bounded arithmetic
Satoru Kuroda
In this paper, we formalize Sprague-Grundy theory for combinatorial games in bounded arithmetic. We show that in the presence of Sprague-Grundy numbers, a fairly weak axioms captur…
cs.LO1999★ 1 cited
Weak length induction and slow growing depth boolean circuits
Satoru Kuroda
We define a hierarchy of circuit complexity classes LD^i, whose depth are the inverse of a function in Ackermann hierarchy. Then we introduce extremely weak versions of length indu…