Diamond (on the regulars) can fail at any strongly unfoldable cardinal

Mirna Džamonja; Joel David Hamkins

doi:10.1016/j.apal.2006.05.001

Diamond (on the regulars) can fail at any strongly unfoldable cardinal

Mirna Džamonja, Joel David Hamkins

Algebra, Number Theory, Logic, and Representations (ANTLR)

Research output: Contribution to journal › Article › peer-review

18 Citations (Scopus)

Abstract

If ? is any strongly unfoldable cardinal, then this is preserved in a forcing extension in which ??(REG) fails. This result continues the progression of the corresponding results for weakly compact cardinals, due to Woodin, and for indescribable cardinals, due to Hauser.

Original language	English
Pages (from-to)	83-95
Number of pages	13
Journal	Annals of Pure and Applied Logic
Volume	144
Issue number	1-3
DOIs	https://doi.org/10.1016/j.apal.2006.05.001
Publication status	Published - 1 Dec 2006

Access to Document

10.1016/j.apal.2006.05.001Licence: Other

http://arxiv.org/abs/math.LO/0409304

Cite this

@article{e7b9fd241a6b451b8eb8ce03692d808b,

title = "Diamond (on the regulars) can fail at any strongly unfoldable cardinal",

abstract = "If ? is any strongly unfoldable cardinal, then this is preserved in a forcing extension in which ??(REG) fails. This result continues the progression of the corresponding results for weakly compact cardinals, due to Woodin, and for indescribable cardinals, due to Hauser.",

author = "Mirna D{\v z}amonja and Hamkins, {Joel David}",

year = "2006",

month = dec,

day = "1",

doi = "10.1016/j.apal.2006.05.001",

language = "English",

volume = "144",

pages = "83--95",

journal = "Annals of Pure and Applied Logic",

publisher = "Elsevier",

number = "1-3",

}

TY - JOUR

T1 - Diamond (on the regulars) can fail at any strongly unfoldable cardinal

AU - Džamonja, Mirna

AU - Hamkins, Joel David

PY - 2006/12/1

Y1 - 2006/12/1

N2 - If ? is any strongly unfoldable cardinal, then this is preserved in a forcing extension in which ??(REG) fails. This result continues the progression of the corresponding results for weakly compact cardinals, due to Woodin, and for indescribable cardinals, due to Hauser.

AB - If ? is any strongly unfoldable cardinal, then this is preserved in a forcing extension in which ??(REG) fails. This result continues the progression of the corresponding results for weakly compact cardinals, due to Woodin, and for indescribable cardinals, due to Hauser.

U2 - 10.1016/j.apal.2006.05.001

DO - 10.1016/j.apal.2006.05.001

M3 - Article

VL - 144

SP - 83

EP - 95

JO - Annals of Pure and Applied Logic

JF - Annals of Pure and Applied Logic

IS - 1-3

ER -