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BERKELEY CARDINALS AND THE STRUCTURE OF L(Vδ+1)

Published online by Cambridge University Press:  21 December 2018

RAFFAELLA CUTOLO
RAFFAELLA CUTOLO*
Affiliation:
DEPARTMENT OF MATHEMATICS AND APPLICATIONS UNIVERSITY OF NAPLES “FEDERICO II” VIA CINTIA 21, 80126 NAPLES, ITALYE-mail: [email protected]
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Abstract

We explore the structural properties of the inner model L(Vδ+1) under the assumption that δ is a singular limit of Berkeley cardinals each of which is itself limit of extendible cardinals, lifting some of the main results of the theory of the axiom I0 to the level of Berkeley cardinals, the strongest known large cardinal axioms. Berkeley cardinals have been recently introduced in [1] and contradict the Axiom of Choice.1 In fact, our background theory will be ZF.

Keywords

03E4503E55Berkeley cardinalschoiceless large cardinalsI0
Type
Articles
Information
The Journal of Symbolic Logic , Volume 83 , Issue 4 , December 2018 , pp. 1457 - 1476
Copyright
Copyright © The Association for Symbolic Logic 2018 

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Footnotes

1

Precisely, it is shown in [1] that if the cofinality of the least Berkeley cardinal equals γ then γ-DC fails, where γ-DC is γ-Dependent Choice.

References

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