12 citations · 22 across the 25 of their papers we have counts for
26 papers
Extendible cardinals, and Laver-generic large cardinal axioms for extendibility
Sakaé Fuchino
We introduce (super--)Laver-generic large cardinal axioms for extendibility ((super--)LgLCAs for extendible, for short), and show that most of the previ…
Reflection and Recurrence
Sakaé Fuchino
We examine the Zermelo Fraenkel set theory with Choice (ZFC) enhanced by one of the (structural) reflection principles down to a small cardinal and/or Recurrence Axioms defined bel…
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 Recurrence Axioms
Sakaé Fuchino, Toshimichi Usuba
The Recurrence Axiom for a class of \pos\ and a set of parameters is an axiom scheme in the language of ZFC asserting that if a statement with parameters from …
Maximality Principles and Ressurection Axioms under a Laver-generic large cardinal
Sakaé Fuchino
Set-theoretic axioms formulated in terms of existence of a Laver-generic large cardinal were introduced in [16] and studied further in [17], [18], [20]. These axioms, let us call t…
Weakly extendible cardinals and compactness of extended logics
Sakaé Fuchino, Hiroshi Sakai
We introduce the notion of weakly extendible cardinals and show that these cardinals are characterized in terms of weak compactness of second order logic. The consistency strength…