18 citations · 38 across the 14 of their papers we have counts for
16 papers
Fragments of SRP, the nonstationary ideal, and diagonal reflection
Gunter Fuchs, Hiroshi Sakai
We investigate the relationships between fragments of SRP and diagonal reflection principles. It turns out that the subcomplete fragment of SRP, augmented with CH, implies that the…
An extension of Subcomplete Forcing Axiom which implies
Hiroshi Sakai
We prove that the Subcomplete Forcing Axiom is consistent with .
On -stationarity of
Hiroshi Sakai, M. Catalina Torres
The notion of -stationary subsets of for were introduced and studied by Cody, Lambie-Hanson \& Zhang \cite{CLHZ} and Torres \cite{T}. They proved that i…
Separating Subversion Forcing Axioms
Hiroshi Sakai, Corey Bacal Switzer
We study a family of variants of Jensen's\emph{subcomplete forcing axiom}, and \emph{subproper forcing axiom}, . Using these we develop a general t…
Weakly extendible cardinals and compactness of extended logics
Sakaé Fuchino, Hiroshi Sakai
We introduce the notion of weakly extendible cardinals and show that these cardinals are characterized in terms of weak compactness of second order logic. The consistency strength…
Generically supercompact cardinals by forcing with chain conditions
Sakaé Fuchino, Hiroshi Sakai
A ccc-generically supercompact cardinal can be smaller than or equal to the continuum. On the other hand, such a cardinal still satisfies diverse largeness properties, like…
Strong downward Löwenheim-Skolem theorems for stationary logics, III -- mixed support iteration
Sakaé Fuchino, André Ottenbreit Maschio Rodrigue, Hiroshi Sakai
Continuing [Fuchino, Ottenbreit and Sakai[9, 10]] and [Fuchino and Ottenbreit[11]], we further study reflection principles in connection with the Löwenheim-Skolem Theorems of stati…
The first-order definability of generic large cardinals
Sakaé Fuchino, Hiroshi Sakai
We show that the notions of generic and Laver-generic supercompactness are first-order definable in the language of ZFC. This also holds for generic and Laver-generic (almost) huge…
Strong downward Löwenheim-Skolem theorems for stationary logics, II -- reflection down to the continuum
Sakaé Fuchino, André Ottenbreit Maschio Rodrigues, Hiroshi Sakai
Continuing the previous paper, we study the Strong Downward Löwenheim-Skolem Theorems (SDLSs) of the stationary logic and their variations. It has been shown that the SDLS for the…
Martin's Maximum and the Diagonal Reflection Principle
Sean Cox, Hiroshi Sakai
We prove that Martin's Maximum does not imply the Diagonal Reflection Principle for stationary subsets of .
A variant of Shelah's characterization of Strong Chang's Conjecture
Sean Cox, Hiroshi Sakai
Shelah considered a certain version of Strong Chang's Conjecture, which we denote , and proved that it is equivalent to several statements, including the a…
The weakly compact reflection principle need not imply a high order of weak compactness
Brent Cody, Hiroshi Sakai
The weakly compact reflection principle states that is a weakly compact cardinal and every weakly compact subset of has a weakly compact proper…
On the set-generic multiverse
Sy David Friedman, Sakaé Fuchino, Hiroshi Sakai
The forcing method is a powerful tool to prove the consistency of set-theoretic assertions relative to the consistency of the axioms of set theory. Laver's theorem and Bukovský's t…
Stationary reflection principles and two cardinal tree properties
Hiroshi Sakai, Boban Velickovic
We study consequences of stationary and semi-stationary set reflection. We show that the semi stationary reflection principle implies the Singular Cardinal Hypothesis, the failure…
Random-Matrix Theory of Electron Transport in Disordered Wires with Symplectic Symmetry
Hiroshi Sakai, Yositake Takane
The conductance of disordered wires with symplectic symmetry is studied by a random-matrix approach. It has been believed that Anderson localization inevitably arises in ordinary d…
Conductance and Its Variance of Disordered Wires with Symplectic Symmetry in the Metallic Regime
Hiroshi Sakai, Yositake Takane
The conductance of disordered wires with symplectic symmetry is studied by a random-matrix approach. It has been shown that the behavior of the conductance in the long-wire limit c…