Results 21 to 30 of about 218 (121)
On the partition property of measures on Pℋλ
International Journal of Mathematics and Mathematical Sciences, Volume 5, Issue 4, Page 817-821, 1982., 1982 The partition property for measures on Pℋλ was formulated by analogy with a property which Rowbottom [1] proved was possessed by every normal measure on a measurable cardinal. This property has been studied in [2], [3], and [4]. This note summarizes [5] and [6], which contain results relating the partition property with the extendibility of the measure
Donald H. Pelletier
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, 2023 A pdf file of updated and extended version of this paper possibly with more details and proofs is downloadable as: https: // fuchino. ddo. jp/papers/RIMS2022-RA-MP-x.
Fuchino, Sakaé
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The Partition Property for Certain Extendible Measures on Supercompact Cardinals [PDF]
Proceedings of the American Mathematical Society, 1981 ABsTRAcr. We give an alternate characterization of a combinatorial property of measures onpKA introduced by Menas. We use this characterization to prove that if K is supercompact, then all measures on pKX in a certain class have the partition property. This result is applied to obtain a self-contained proof that if K iS supercompact and X is the least ...
openaire +2 more sources
Indestructibility and c(n)-supercompact cardinals [PDF]
, 2023 This thesis is split into two areas of interest. The first, a study of indestructibility results for two variants of supercompactness; the second, a discussion of double-membership graphs of models of Anti-Foundational set theory. In Chapter 3 we will
Adam-Day, Beatrice
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Weak compactness cardinals for strong logics and subtlety properties of the class of ordinals
Journal of the London Mathematical Society, Volume 112, Issue 1, July 2025.Abstract Motivated by recent work of Boney, Dimopoulos, Gitman, and Magidor, we characterize the existence of weak compactness cardinals for all abstract logics through combinatorial properties of the class of ordinals. This analysis is then used to show that, in contrast to the existence of strong compactness cardinals, the existence of weak ...
Philipp Lücke
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A Cellular Constraint in Supercompact Hausdorff Spaces
, 1978 In this paper we prove a cardinal inequality for supercompact Uausdorff spaces which gives insight into the cellular structure of such spaces and yields new examples of compact Uausdorff non-supercompact spaces.
Murray G. Bell
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Cardinal characteristics at in a small u (κ) model [PDF]
, 2017 We provide a model where u(κ)
Fischer, V +7 more
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Full Souslin trees at small cardinals
Journal of the London Mathematical Society, Volume 110, Issue 1, July 2024.Abstract A κ$\kappa$‐tree is full if each of its limit levels omits no more than one potential branch. Kunen asked whether a full κ$\kappa$‐Souslin tree may consistently exist. Shelah gave an affirmative answer of height a strong limit Mahlo cardinal κ$\kappa $. Here, it is shown that these trees may consistently exist at small cardinals. Indeed, there
Assaf Rinot, Shira Yadai, Zhixing You
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Bulletin of the London Mathematical Society, Volume 56, Issue 6, Page 1967-1987, June 2024.Abstract We investigate connections between set‐theoretic compactness principles and cardinal arithmetic, introducing and studying generalized narrow system properties as a way to approach two open questions about two‐cardinal tree properties. The first of these questions asks whether the strong tree property at a regular cardinal κ⩾ω2$\kappa \geqslant
Chris Lambie‐Hanson
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Journal of the London Mathematical Society, Volume 109, Issue 6, June 2024.Abstract We demonstrate that the technology of Radin forcing can be used to transfer compactness properties at a weakly inaccessible but not strong limit cardinal to a strongly inaccessible cardinal. As an application, relative to the existence of large cardinals, we construct a model of set theory in which there is a strongly inaccessible cardinal κ ...
Tom Benhamou, Jing Zhang
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