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pro vyhledávání: '"Levine, Maxwell"'
Autor:
Levine, Maxwell
We build on a 1990 paper of Bukovsky and Coplakova-Hartova. First, we remove the hypothesis of $\textsf{CH}$ from one of their minimality results. Then, using a measurable cardinal, we show that there is a $|\aleph_2^V|=\aleph_1$-minimal extension th
Externí odkaz:
http://arxiv.org/abs/2408.03487
Autor:
Jakob, Hannes, Levine, Maxwell
Krueger showed that PFA implies that for all regular $\Theta \ge \aleph_2$, there are stationarily many $[H(\Theta)]^{\aleph_1}$ that are internally club but not internally approachable. From countably many Mahlo cardinals, we force a model in which,
Externí odkaz:
http://arxiv.org/abs/2404.15230
Autor:
Levine, Maxwell
We show that it is consistent from an inaccessible cardinal that classical Namba forcing has the weak $\omega_1$-approximation property. In fact, this is the case if $\aleph_1$-preserving forcings do not add cofinal branches to $\aleph_1$-sized trees
Externí odkaz:
http://arxiv.org/abs/2312.14083
Autor:
Levine, Maxwell
Publikováno v:
Pacific J. Math. 332 (2024) 147-165
We answer a question of Krueger by obtaining disjoint stationary sequences on successive cardinals. The main idea is an alternative presentation of a mixed support iteration, using it even more explicitly as a variant of Mitchell forcing. We also use
Externí odkaz:
http://arxiv.org/abs/2301.02634
Autor:
Levine, Maxwell
We introduce a forcing that adds a $\square(\aleph_2,\aleph_0)$-sequence with countable conditions under CH. Assuming the consistency of a weakly compact cardinal, we can find a forcing extension by our new poset in which both $\square(\aleph_2,<\!\a
Externí odkaz:
http://arxiv.org/abs/2209.12258
Autor:
Levine, Maxwell
Cummings, Foreman, and Magidor proved that Jensen's square principle is non-compact at $\aleph_\omega$, meaning that it is consistent that $\square_{\aleph_n}$ holds for all $n<\omega$ while $\square_{\aleph_\omega}$ fails. We investigate the natural
Externí odkaz:
http://arxiv.org/abs/2208.09380
Autor:
Levine, Maxwell, Mildenberger, Heike
Dobrinen, Hathaway and Prikry studied a forcing $\mathbb{P}_\kappa$ consisting of perfect trees of height $\lambda$ and width $\kappa$ where $\kappa$ is a singular $\omega$-strong limit of cofinality $\lambda$. They showed that if $\kappa$ is singula
Externí odkaz:
http://arxiv.org/abs/2110.03648
Autor:
Droll, Stephenie H., Zhang, Benny J., Levine, Maxwell C., Xue, Celia, Ho, Patric J., Bao, Xiaomin
Publikováno v:
In Journal of Investigative Dermatology September 2024 144(9):2029-2038
We obtain an array of consistency results concerning trees and stationary reflection at double successors of regular cardinals $\kappa$, updating some classical constructions in the process. This includes models of $\mathsf{CSR}(\kappa^{++})\wedge \m
Externí odkaz:
http://arxiv.org/abs/2103.15728
Autor:
Levine, Maxwell, Rinot, Assaf
We address the question of whether a reflecting stationary set may be partitioned into two or more reflecting stationary subsets, providing various affirmative answers in ZFC. As an application to singular cardinals combinatorics, we infer that it is
Externí odkaz:
http://arxiv.org/abs/1907.08581