Hiroshi Sakai

collaborators

2 papers

math.LO2025

Perfect set dichotomy theorem in generalized Solovay model

Hiroshi Sakai, Toshimasa Tanno

We prove that the perfect set dichotomy theorem holds in the Solovay model $V ((I ¨ ^{I ¨} )^{V [G]})$ . Namely, for every equivalence relation $E$ on $R$ , either $R / E$ i…

math.LO2025

Generalized Tukey reducibility between $I ¨ $ -directed sets

Hiroshi Sakai, Toshimasa Tanno

We introduce the pre-Tukey reducibility, a generalization of the Tukey reducibility between directed sets that works well in $ZF$ . We investigate the pre-Tukey reducibilit…

Perfect set dichotomy theorem in generalized Solovay model

Generalized Tukey reducibility between I¨-directed sets

Generalized Tukey reducibility between $I ¨ $ -directed sets