10 papers · 1 filter
Variants of Łoś's Theorem
Toshimichi Usuba
We study Łoś's theorem in a choiceless context. We introduce some variants of Łoś's theorem. These variants seem weaker than Łoś's theorem, but we prove that these are equivalent t…
On Countable Stationary Towers
Yo Matsubara, Toshimichi Usuba
In this paper, we investigate properties of countable stationary towers. We derive the regularity properties of sets of reals in from some properties of countable st…
A note on Löwenheim-Skolem cardinals
Toshimichi Usuba
In this note we provide some applications of Löwenheim-Skolem cardinals introduced in \cite{U}.
A note on -strongly compact cardinals
Toshimichi Usuba
In this paper we investigate more characterizations and applications of -strongly compact cardinals. We show that, for a cardinal the following are equivalent: (1) is $δ…
Geology of symmetric grounds
Toshimichi Usuba
Let us say that a model of is a symmetric ground if is a symmetric extension of the model. In this paper, we investigate set-theoretic geology of symmetric ground…
Choiceless Löwenheim-Skolem property and uniform definability of grounds
Toshimichi Usuba
In this paper, without the axiom of choice, we show that if a certain downward Löwenheim-Skolem property holds then all grounds are uniformly definable. We also prove that the axio…