Zobrazeno 1 - 10
of 159
pro vyhledávání: '"Garti, Shimon"'
Autor:
Garti, Shimon, Shelah, Saharon
Publikováno v:
Comptes Rendus. Mathématique, Vol 361, Iss G5, Pp 853-861 (2023)
We show that one can force superclub with an arbitrarily large value of $\mathrm{cov}(\mathscr{M})$. We prove that the club principle is consistent with an arbitrarily large value of $\mathrm{add}(\mathscr{M})$. We also prove that if $\kappa $ is reg
Externí odkaz:
https://doaj.org/article/2576890dca6b414ba0788db6b7495d27
Autor:
Garti, Shimon
We obtain bounds on the cardinality of $pcf(\mathfrak{a})$ from instances of weak diamond. Consequently, under mild assumptions there are many singular cardinals of the from $\aleph_\delta$ for which $2^{\aleph_\delta}<\aleph_{(|\delta|^{+3})}$. For
Externí odkaz:
http://arxiv.org/abs/2405.03142
Autor:
Garti, Shimon
We prove a positive polarized cube relation for infinite cardinals.
Comment: To appear
Comment: To appear
Externí odkaz:
http://arxiv.org/abs/2404.18888
Autor:
Garti, Shimon
Addressing a question of Paul Larson we prove the following statement. If Chang's conjecture fails, Martin's axiom holds and the continuum is greater than $\aleph_2$, there are no weakly Laver ideals over $\aleph_1$. We also prove that under Baumgart
Externí odkaz:
http://arxiv.org/abs/2401.13364
Autor:
Garti, Shimon
Publikováno v:
Periodica Mathematica Hungarica, volume 88 (1), March 2024, pp. 137-147
We prove the consistency of tiltan with the positive relation $\omega^*\cdot\omega_1\rightarrow(\omega^*\cdot\omega_1,{\rm infinite\ path})^2$.
Comment: References
Comment: References
Externí odkaz:
http://arxiv.org/abs/2302.09492
Autor:
Garti, Shimon, Shelah, Saharon
We prove that superclub implies $\mathfrak{s}=\aleph_1$. More generally, superclub at a successor of a weakly compact cardinal implies $\mathfrak{s}_\kappa=\kappa^+$. Based on this statement, we separate tiltan from superclub at a successor of a supe
Externí odkaz:
http://arxiv.org/abs/2302.00904
Autor:
Garti, Shimon, Villaveces, Andrés
Publikováno v:
Bulletin of the Belgian Mathematical Society - Simon Stevin, vol. 30 (4), pp. 456-467, December 2023
Let $\mu$ be a strong limit singular cardinal. We prove that if $2^{\mu} > \mu^+$ then $\binom{\mu^+}{\mu}\to \binom{\tau}{\mu}_{<{\rm cf}(\mu)}$ for every ordinal $\tau<\mu^+$. We obtain an optimal positive relation under $2^\mu = \mu^+$, as after c
Externí odkaz:
http://arxiv.org/abs/2301.12413
We address the question of the consistency strength of certain filters and ultrafilters which fail to satisfy the Galvin property. We answer questions \cite[Questions 7.8,7.9]{TomMotiII}, \cite[Question 5]{NegGalSing} and improve theorem \cite[Theore
Externí odkaz:
http://arxiv.org/abs/2211.00116
In the first part of this paper, we explore the possibility for a very large cardinal $\kappa$ to carry a $\kappa$-complete ultrafilter without Galvin's property. In this context, we prove the consistency of every ground model $\kappa$-complete ultra
Externí odkaz:
http://arxiv.org/abs/2207.07401
Publikováno v:
Journal of the London Mathematical Society, volume 108 (1), pp. 190-237, July 2023
We prove that Galvin's property consistently fails at successors of strong limit singular cardinals. We also prove the consistency of this property failing at every successor of a singular cardinal. In addition, the paper analyzes the effect of Prikr
Externí odkaz:
http://arxiv.org/abs/2112.13373