LOCAL CLUB CONDENSATION AND L-LIKENESS

doi:10.1017/jsl.2015.6

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	LOCAL CLUB CONDENSATION AND L-LIKENESS
	Holy, Peter 1; Welch, Philip 2; Wu, Liuzhen3
	2015-12-01
发表期刊	JOURNAL OF SYMBOLIC LOGIC
ISSN	0022-4812
卷号	80 期号:4 页码:1361-1378
摘要	We 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.
关键词	Condensation L-like model Square Chang's Conjecture Forcing Erdos cardinal Interleaving Structures
DOI	10.1017/jsl.2015.6
语种	英语
资助项目	EPSRC[EP/J005630/1] ; FWF[P23875-N13] ; CNSF[11321101]
WOS研究方向	Mathematics ; Science & Technology - Other Topics
WOS类目	Mathematics ; Logic
WOS记录号	WOS:000367382200015
出版者	CAMBRIDGE UNIV PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/21683
专题	数学所
通讯作者	Holy, Peter
作者单位	1.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
推荐引用方式 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.