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math.LO2024
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…
math.LO2024
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…
math.LO2024
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 …