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LOCAL CLUB CONDENSATION AND L-LIKENESS
Holy, Peter1; Welch, Philip2; Wu, Liuzhen3
2015-12-01
Source PublicationJOURNAL OF SYMBOLIC LOGIC
ISSN0022-4812
Volume80Issue:4Pages:1361-1378
AbstractWe present a forcing to obtain a localized version of Local Club Condensation, a generalized Condensation principle introduced by Sy Friedman and the first author in [3] and [5]. This forcing will have properties nicer than the forcings to obtain this localized version that could be derived from the forcings presented in either [3] or [5]. We also strongly simplify the related proofs provided in [3] and [5]. Moreover our forcing will be capable of introducing this localized principle at kappa while simultaneously performing collapses to make kappa become the successor of any given smaller regular cardinal. This will be particularly useful when kappa has large cardinal properties in the ground model. We will apply this to measure how much L-likeness is implied by Local Club Condensation and related principles. We show that Local Club Condensation at kappa(+) is consistent with inverted left perpendicular square(kappa) whenever kappa is regular and uncountable, generalizing and improving a result of the third author in [14], and that if kappa >= omega(2) is regular, CC(kappa(+)) - Chang's Conjecture at kappa(+) - is consistent with Local Club Condensation at kappa(+), both under suitable large cardinal consistency assumptions.
KeywordCondensation L-like model Square Chang's Conjecture Forcing Erdos cardinal Interleaving Structures
DOI10.1017/jsl.2015.6
Language英语
Funding ProjectEPSRC[EP/J005630/1] ; FWF[P23875-N13] ; CNSF[11321101]
WOS Research AreaMathematics ; Science & Technology - Other Topics
WOS SubjectMathematics ; Logic
WOS IDWOS:000367382200015
PublisherCAMBRIDGE UNIV PRESS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/21683
Collection数学所
Affiliation1.Univ Bonn, Math Inst, D-53115 Bonn, Germany
2.Univ Bristol, Dept Math, Bristol BS8 1TW, Avon, England
3.Chinese Acad Sci, Inst Math, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Holy, Peter,Welch, Philip,Wu, Liuzhen. LOCAL CLUB CONDENSATION AND L-LIKENESS[J]. JOURNAL OF SYMBOLIC LOGIC,2015,80(4):1361-1378.
APA Holy, Peter,Welch, Philip,&Wu, Liuzhen.(2015).LOCAL CLUB CONDENSATION AND L-LIKENESS.JOURNAL OF SYMBOLIC LOGIC,80(4),1361-1378.
MLA Holy, Peter,et al."LOCAL CLUB CONDENSATION AND L-LIKENESS".JOURNAL OF SYMBOLIC LOGIC 80.4(2015):1361-1378.
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