Tatsuya Goto

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20212026

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math.LO2026

Borel-Tukey morphisms between Ramsey homogeneity relations

Tatsuya Goto

We study Borel-Tukey morphisms between almost-homogeneity relations. For finite $r, s \geq 1$ and $m, n \geq 2$ , we give the complete one-stage classification: $\mathbf{Hom}^r_m\to_{\mathr…

math.LO2026

Two variants of minimality in forcing extensions

Martin Goldstern, Tatsuya Goto

We introduce d-minimal and b-minimal extensions, two weakenings of minimality based respectively on eventual domination and infinitely often domination. We prove that the generic e…

math.LO2026

Forcing and Cardinal Invariants of Universally Null Sets

Tatsuya Goto

We study universally null sets in forcing extensions and the cardinal invariants of their ideal $UN$ . We prove that the Miller model contains a nonmeager universally null…

math.LO2023

Game-theoretic variants of cardinal invariants

Jorge Antonio Cruz Chapital, Tatsuya Goto, Yusuke Hayashi

We investigate game-theoretic variants of cardinal invariants of the continuum. The invariants we treat are the reaping number $r$ , the bounding number $b$ , t…

math.LO2023

The comparability numbers and the incomparability numbers

Tatsuya Goto

We introduce new cardinal invariants of a poset, called the comparability number and the incomparability number. We determine their value for well-known posets, such as $ω^{ω}$ , $\ma…

math.LO2022

Goldstern's principle about unions of null sets

Tatsuya Goto

Goldstern showed in his 1993 paper that the union of a real-parametrized, monotone family of Lebesgue measure zero sets has also Lebesgue measure zero provided that the sets are un…