A new large cardinal and Laver sequences for extendibles

• Autorzy: Paul Corazza
• Języki publikacji: EN

Abstrakty

EN

We define a new large cardinal axiom that fits between $A_3$ and $A_4$ in the hierarchy of axioms described in [SRK]. We use this new axiom to obtain a Laver sequence for extendible cardinals, improving the known large cardinal upper bound for the existence of such sequences.

Kategorie tematyczne

• 03E55: Large cardinals
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1997
• Tom: 152
• Numer: 2
• Strony: 183-188

Daty

wydano

1997

otrzymano

1996-07-08

poprawiono

1996-08-22

Twórcy

autor

Paul Corazza

• Department of Mathematics, Maharishi University of Management, Fairfield, Iowa 52557, U.S.A.

Bibliografia

• [C] P. Corazza, The wholeness axiom and Laver sequences, Ann. Pure Appl. Logic, 98 pp., submitted.
• [GS] M. Gitik, and S. Shelah, On certain indestructibility of strong cardinals and a question of Hajnal, Arch. Math. Logic 28 (1989), 35-42.
• [K] A. Kanamori, The Higher Infinite, Springer, New York, 1994.
• [L] R. Laver, Making the supercompactness of κ indestructible under κ-directed closed forcing, Israel J. Math. 29 (1978), 385-388.
• [SRK] R. Solovay, W. Reinhardt and A. Kanamori, Strong axioms of infinity and elementary embeddings, Ann. Math. Logic 13 (1978), 73-116.