Tetsuya Ishiu

Directive trees and games on posets

We show that for any infinite cardinal κ, every (κ+1)-strategically closed poset is κ + -strategically closed if and only if □ κ holds. This extends previous results of Velleman, et.al.

The comparison of various club guessing principles

Abstract We investigate variations of the club guessing principle, and show that most of the trivial implications cannot be reversed.

The termination of the higher-dimensional tarai functions

We prove that for every integer n ? 3 , the n-dimensional tarai function, proposed by D. Knuth, terminates with call-by-need. The proof is formalized by Coq. We investigate higher-dimensional tarai functions, defined be D. Knuth.We prove that for every n ? 3 , n-dimensional tarai function terminates with call-by-need.No details are provided, but we gave a formal proof to this theorem by Coq.

The saturation of club guessing ideals

Abstract We prove that it is consistent that there exists a saturated tail club guessing ideal on ω 1 which is not a restriction of the non-stationary ideal. Two proofs are presented. The first one uses a new forcing axiom whose consistency can be proved from a supercompact cardinal. The resulting model can satisfy either CH or 2 ℵ 0 = ℵ 2 . The second one is a direct proof from a Woodin cardinal, which gives a witnessing model with CH.