D. Ikegami

collaborators

2 papers

math.LO2021

$I$ -regularity, determinacy, and $\infty$ -Borel sets of reals

Daisuke Ikegami

We show under $ZF + DC + AD_{R}$ that every set of reals is $I$ -regular for any $σ$ -ideal $I$ on the Baire space $ω^{ω}$ such that $P_{I}$ is proper. T…

math.LO2019

On supercompactness of $ω_{1}$

Daisuke Ikegami, Nam Trang

This paper studies structural consequences of supercompactness of $ω_{1}$ under $ZF$ . We show that the Axiom of Dependent Choice $(DC)$ follows from " $ω_{1}$ is supercompact"…

I-regularity, determinacy, and ∞-Borel sets of reals

On supercompactness of ω1​

$I$ -regularity, determinacy, and $\infty$ -Borel sets of reals

On supercompactness of $ω_{1}$