Daisuke Ikegami

activity

20232025

collaborators

3 papers

math.LO2025

Boolean-valued second-order logic revisited

Daisuke Ikegami

Following the paper~[3] by Väänänen and the author, we continue to investigate on the difference between Boolean-valued second-order logic and full second-order logic. We show that…

math.LO2024

Universally Baire sets in $2^{κ}$

Daisuke Ikegami, Matteo Viale

We generalize the basic theory of universally Baire sets of $2^{ω}$ to a theory of universally Baire subsets of $2^{κ}$ . We show that the fundamental characterizations of the property…

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…

Boolean-valued second-order logic revisited

Universally Baire sets in 2κ

Preservation of AD via forcings

Universally Baire sets in $2^{κ}$