Toshimasa Tanno

collaborators

3 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 $V ((ω^{ω})^{V [G]})$ . Namely, for every equivalence relation $E$ on $R$ , either $R / E$ is…

math.LO2025

Generalized Tukey reducibility between $σ$ -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…

math.LO2023

Stationary tower forcings and universally Baire sets

Toshimasa Tanno

We investigate properties of stationary tower forcings and give conditions on stationary towers to derive the universally Baireness of sets of reals in $L (R)$ .

Perfect set dichotomy theorem in generalized Solovay model

Generalized Tukey reducibility between σ-directed sets

Stationary tower forcings and universally Baire sets

Generalized Tukey reducibility between $σ$ -directed sets