1 citations · 1 across the 6 of their papers we have counts for
6 papers
Preservation of AD via forcings
Daisuke Ikegami, Nam Trang
We show that assuming "", any poset which increases does not preserve the truth of . We…
Forcing over choiceless models and generic absoluteness
Daisuke Ikegami, Philipp Schlicht
We develop a toolbox for forcing over arbitrary models of set theory without the axiom of choice. In particular, we introduce a variant of the countable chain condition and prove a…
-regularity, determinacy, and -Borel sets of reals
Daisuke Ikegami
We show under that every set of reals is -regular for any -ideal on the Baire space such that is proper. T…
On supercompactness of
Daisuke Ikegami, Nam Trang
This paper studies structural consequences of supercompactness of under . We show that the Axiom of Dependent Choice follows from " is supercompact"…
Borel subsets of the real line and continuous reducibility
Daisuke Ikegami, Philipp Schlicht, Hisao Tanaka
We study classes of Borel subsets of the real line such as levels of the Borel hierarchy and the class of sets that are reducible to the set of rationals,…
On a class of maximality principles
Daisuke Ikegami, Nam Trang
We study various classes of maximality principles, , introduced by J.D. Hamkins, where defines a class of forcing posets and is a cardinal. We explore the con…