Yasuo Yoshinobu

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Empty p0 p2 . . . pξ pξ+2 . . . Nonempty p1 p3 . . . pξ+1 pξ+3 . . . where pξ, ξ < α, is descending in P and Nonempty wins the game of length α if he can play α times. A poset P is called weakly α-game-closed if Player Nonempty has a winning strategy in the Banach-Mazur game of length α, where Nonempty is allowed to play at limit stages. P is called(More)
It is known that the Stone-Čech compactification βX of a noncompact metrizable space X is approximated by the collection of Smirnov compactifications of X for all compatible metrics on X. We investigate the smallest cardinality of a set D of compatible metrics on the countable discrete space ω such that, βω is approximated by Smirnov compactifications for(More)
It is known that the Stone–Čech compactification βX of a metrizable space X is approximated by the collection of Smirnov compactifications of X for all compatible metrics on X. If we confine ourselves to locally compact separable metrizable spaces, the corresponding statement holds for Higson compactifications. We investigate the smallest cardinality of a(More)
It is known that the Stone–Čech compactification βX of a metrizable space X is approximated by the collection of Smirnov compactifications of X for all compatible metrics on X. If we confine ourselves to locally compact separable metrizable spaces, the corresponding statement holds for Higson compactifications. We investigate the smallest cardinality of a(More)
We present several forcing posets for adding a non-reflecting stationary subset of Pω1 (λ), where λ ≥ ω2. We prove that PFA is consistent with dense non-reflection in Pω1 (λ), which means that every stationary subset of Pω1 (λ) contains a stationary subset which does not reflect to any set of size א1. If λ is singular with countable cofinality, then dense(More)