A new large cardinal and Laver sequences for extendibles

Paul Corazza

Fundamenta Mathematicae (1997)

  • Volume: 152, Issue: 2, page 183-188
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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Corazza, Paul. "A new large cardinal and Laver sequences for extendibles." Fundamenta Mathematicae 152.2 (1997): 183-188. <http://eudml.org/doc/212205>.

@article{Corazza1997,
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.},
author = {Corazza, Paul},
journal = {Fundamenta Mathematicae},
keywords = {hierarchy of large-cardinal axioms; large cardinal axiom; Laver sequence for extendible cardinals},
language = {eng},
number = {2},
pages = {183-188},
title = {A new large cardinal and Laver sequences for extendibles},
url = {http://eudml.org/doc/212205},
volume = {152},
year = {1997},
}

TY - JOUR
AU - Corazza, Paul
TI - A new large cardinal and Laver sequences for extendibles
JO - Fundamenta Mathematicae
PY - 1997
VL - 152
IS - 2
SP - 183
EP - 188
AB - 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.
LA - eng
KW - hierarchy of large-cardinal axioms; large cardinal axiom; Laver sequence for extendible cardinals
UR - http://eudml.org/doc/212205
ER -

References

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  1. [C] P. Corazza, The wholeness axiom and Laver sequences, Ann. Pure Appl. Logic, 98 pp., submitted. Zbl0999.03048
  2. [GS] M. Gitik, and S. Shelah, On certain indestructibility of strong cardinals and a question of Hajnal, Arch. Math. Logic 28 (1989), 35-42. Zbl0663.03041
  3. [K] A. Kanamori, The Higher Infinite, Springer, New York, 1994. Zbl0813.03034
  4. [L] R. Laver, Making the supercompactness of κ indestructible under κ-directed closed forcing, Israel J. Math. 29 (1978), 385-388. Zbl0381.03039
  5. [SRK] R. Solovay, W. Reinhardt and A. Kanamori, Strong axioms of infinity and elementary embeddings, Ann. Math. Logic 13 (1978), 73-116. Zbl0376.02055

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