6 papers
Cardinal invariants of idealized Miller null sets
Aleksander CieÅlak, Takehiko Gappo, Arturo MartÃnez-Celis +1
This paper provides an extensive study of the -Miller null ideals , -ideals on the Baire space parametrized by ideals on countable set…
Long games just beyond fixed countable length
Takehiko Gappo, Sandra Müller
We introduce a new type of game on natural numbers of variable countable length, which can be regarded as a diagonalization of all games of fixed countable length on natural number…
Separating Maximality Principles
Takehiko Gappo, Andreas Lietz
We investigate fragments of generic absoluteness principles known as Maximality Principles. We determine the consistency strength of - and -$\ma…
Generic Absoluteness Revisited
Sakaé Fuchino, Takehiko Gappo, Francesco Parente
The present paper is concerned with the relation between recurrence axioms and Laver-generic large cardinal axioms in light of principles of generic absoluteness and the Ground Axi…
On -strongly measurable cardinals in extensions
Navin Aksornthong, Takehiko Gappo, James Holland +1
We show that in the extension of a certain Chang-type model of determinacy, if , then the restriction of the club filter on $κ\cap\m…
Chang models over derived models with supercompact measures
Takehiko Gappo, Sandra Müller, Grigor Sargsyan
Based on earlier work of the third author, we construct a Chang-type model with supercompact measures extending a derived model of a given hod mouse with a regular cardinal th…