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math.LO2020
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…
math.LO2020
The list-chromatic number and the coloring number of uncountable graphs
Toshimichi Usuba
We study the list-chromatic number and the coloring number of graphs, especially uncountable graphs. We show that the coloring number of a graph coincides with its list-chromatic n…
math.LO2020
A note on Löwenheim-Skolem cardinals
Toshimichi Usuba
In this note we provide some applications of Löwenheim-Skolem cardinals introduced in \cite{U}.
math.LO2020
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…