共查询到20条相似文献,搜索用时 15 毫秒
1.
Albin L. Jones 《Proceedings of the American Mathematical Society》2008,136(4):1445-1449
We prove that if and , then for all . This polarized partition relation holds if for every partition either there are and with or there are and with .
2.
Universal indestructibility for degrees of supercompactness and strongly compact cardinals 总被引:1,自引:1,他引:0
We establish two theorems concerning strongly compact cardinals and universal indestructibility for degrees of supercompactness.
In the first theorem, we show that universal indestructibility for degrees of supercompactness in the presence of a strongly
compact cardinal is consistent with the existence of a proper class of measurable cardinals. In the second theorem, we show
that universal indestructibility for degrees of supercompactness is consistent in the presence of two non-supercompact strongly
compact cardinals, each of which exhibits a significant amount of indestructibility for its strong compactness.
The first author’s research was partially supported by PSC-CUNY grants and CUNY Collaborative Incentive grants. The first
author wishes to thank James Cummings for helpful discussions on the subject matter of this paper. In addition, both authors
wish to thank the referee, for many helpful comments and suggestions which were incorporated into the current version of the
paper. 相似文献
3.
James M. Henle 《Mathematical Logic Quarterly》2006,52(6):585-594
In [1] it was shown that if κ is a strong partition cardinal, then every function from [κ ]κ to [κ ]κ is continuous almost everywhere. In this investigation, we explore whether such functions are differentiable or integrable in any sense. Some of them are. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
4.
Lorenz Halbeisen 《Archive for Mathematical Logic》2018,57(5-6):593-599
For a set M, let \({\text {seq}}(M)\) denote the set of all finite sequences which can be formed with elements of M, and let \([M]^2\) denote the set of all 2-element subsets of M. Furthermore, for a set A, let Open image in new window denote the cardinality of A. It will be shown that the following statement is consistent with Zermelo–Fraenkel Set Theory \(\textsf {ZF}\): There exists a set M such that Open image in new window and no function Open image in new window is finite-to-one. 相似文献
5.
6.
M. Rajagopalan 《Israel Journal of Mathematics》1976,23(2):117-125
A compactT
2 spaceX which is separable, scattered and uncountable, but still so thatX
α−Xα+1is countable for all α∈[1, ω) is constructed. This answers one of the problems presented by M. E. Rudin in a conference as
an open problem and attributed by her to Telgarsky.
The author acknowledges a faculty research grant from Memphis State University when this paper was written. 相似文献
7.
Marion Scheepers 《Order》1990,7(1):41-64
We introduce a partition relation which is an alternate for measuring how badly the ordinary partition relation fails, we develop its corresponding partition calculus and we determine its status for various typical partially ordered sets. 相似文献
8.
Arthur W. Apter 《Israel Journal of Mathematics》1980,35(3):225-233
We prove that under the assumption of a supercompact cardinal κ which is a limit of supercompact cardinals, for any increasing
Σ2 function φ the set {∂<κ:∂ is at least φ(∂) supercompact, is strongly compact, yet is not fully supercompact} is unbounded
in κ. We then use ideas of Magidor to show that under the hypotheses of a supercompact cardinal which is a limit of supercompact
cardinals it is consistent for the least strongly compact cardinal κ0 to be at least φ(κ0) supercompact yet not to be fully supercompact, where φ is again an increasing Σ2 function which also meets certain other technical restrictions.
The author wishes to thank Menachem Magidor for helpful conversations and suggestions in method which were used in the proof
of Theorem 2. 相似文献
9.
Jan Šaroch 《Mathematical Logic Quarterly》2015,61(3):196-201
We prove that the property characterizes Σ‐algebraically compact modules if is not ω‐measurable. Moreover, under a large cardinal assumption, we show that over any ring R where is not ω‐measurable, any free module M of ω‐measurable rank satisfies , hence the assumption on cannot be dropped in general (e.g., over small non‐right perfect rings). In this way, we extend results from a recent paper by Simion Breaz 4 . 相似文献
10.
We address partition problems of Erd?s and Hajnal by showing that for all , if and carries a -dense ideal. If is measurable we show that for where is a very large ordinal less than that is closed under all primitive recursive ordinal operations.
Received: 27 June 2001 / Revised version: 5 December 2001 / Published online: 4 February 2003
The first author was partially supported by NSF grant DMS-0101155 and the Equipe d'Analyse Univ. of Paris 6. The second author
was partially supported by NSF grants DMS-0072560 and DMS-9704477. 相似文献
11.
We study the first cardinalκ satisfying a partition relation defined on the set of finite sequences of smaller ordinals. We show that the fact that this
cardinal is ℵω is equiconsistent with the existence of a measurable cardinal. Under GCH, this cardinal must be inaccessible if it has uncountable
cofinality. It is shown that the GCH assumption is necessary here. 相似文献
12.
13.
Small compact perturbation of strongly irreducible operators 总被引:4,自引:0,他引:4
An operatorT onH is called strongly irreducible ifT is not similar to any reducible operators. In this paper, we shall say yes to answer the following question raised by D. A. Herrero.Given an operatorT with connected spectrum (T) and a positive number , can we find a compact operatorK with K < such thatT+K is strongly irreducible?Supported by National Natural Science Foundation of China(19901011), Mathematical Center of State Education Commission of China and 973 Project of China 相似文献
14.
Quasitriangular + small compact = strongly irreducible 总被引:2,自引:0,他引:2
You Qing Ji 《Transactions of the American Mathematical Society》1999,351(11):4657-4673
Let be a bounded linear operator acting on a separable infinite dimensional Hilbert space. Let be a positive number. In this article, we prove that the perturbation of by a compact operator with can be strongly irreducible if is a quasitriangular operator with the spectrum connected. The Main Theorem of this article nearly answers the question below posed by D. A. Herrero.
Suppose that is a bounded linear operator acting on a separable infinite dimensional Hilbert space with connected. Let be given. Is there a compact operator with such that is strongly irreducible?
15.
Alan D Taylor 《Journal of Combinatorial Theory, Series A》1976,21(2):137-146
We prove a canonical partition relation for finite subsets of ω that generalizes Hindman's theorem in much the same way that the Erdös-Rado canonical partition relation generalizes Ramsey's theorem. As an application of this we establish a generalized pigeon-hole principle for infinite dimensional vector spaces over the two element field. 相似文献
16.
Hajime Urakawa 《Mathematische Zeitschrift》1994,216(1):541-573
Dedicated to Professor Noboru Tanaka in his sixtieth birthday 相似文献
17.
Pé ter Komjá th Mikló s Laczkovich 《Proceedings of the American Mathematical Society》2002,130(5):1487-1491
(GCH) For every cardinal there exists such that for every , there are such that .
18.
Jan Tryba 《Israel Journal of Mathematics》1981,40(3-4):193-196
It is proved that every regular Rowbottom cardinal which is greater than the continuum is strongly inaccessible. We notice
that the theory “ZFC + every cardinal of cofinality ω is Rowbottom” is inconsistent. This answers a question raised by C.
C. Chang and H. J. Keisler. 相似文献
19.
Saharon Shelah 《Israel Journal of Mathematics》1975,20(1):1-12
We solved questions of Erdös and Hajnal and deal with related topics. In particular, we show (CH) that in an example ofN→[N] 3 2 , there need not be a triangle with three colours. 相似文献
20.