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math.LO2023
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…
math.LO2023
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…