D. Ikegami

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20192023

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math.LO2023

Preservation of AD via forcings

Daisuke Ikegami, Nam Trang

We show that assuming $ZF + AD^{+} +$ " $V = L (℘ (R))$ ", any poset which increases $Θ$ does not preserve the truth of $AD$ . We…

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"…

Preservation of AD via forcings

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

On supercompactness of ω1​

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

On supercompactness of $ω_{1}$