A new large cardinal and Laver sequences for extendibles

Paul Corazza

ArticleOriginal scientific text

Title

A new large cardinal and Laver sequences for extendibles

Authors ¹

Affiliations

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

Abstract

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.

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[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.

Title

A new large cardinal and Laver sequences for extendibles

Affiliations

Abstract

Bibliography