Zobrazeno 1 - 10
of 57
pro vyhledávání: '"Benhamou, Tom"'
Autor:
Benhamou, Tom, Sinapova, Dima
Combining stationary reflection (a compactness property) with the failure of SCH (an instance of non-compactness) has been a long-standing theme. We obtain this at $\aleph_{\omega_1}$, answering a question of Ben-Neria, Hayut, and Unger: We prove fro
Externí odkaz:
http://arxiv.org/abs/2411.09048
Autor:
Benhamou, Tom
We characterize the Tukey order, the Galvin property/ Cohesive ultrafilters from \cite{Kanamori1978} in terms of ultrapowers. We use this characterization to measure the distance between the Tukey order and other well-known orders of ultrafilters. Se
Externí odkaz:
http://arxiv.org/abs/2410.06275
Autor:
Benhamou, Tom, Poveda, Alejandro
We develop the non-normal variations of two classical Prikry-type forcings; namely, Magidor and Radin forcings. We generalize the fact that the non-normal Prikry forcing is a projection of the extender-based to a coordinate of the extender to our for
Externí odkaz:
http://arxiv.org/abs/2405.16704
Autor:
Benhamou, Tom, Wu, Fanxin
We provide two types of guessing principles for ultrafilter ($\diamondsuit^{-}_{\lambda}(U), \ \diamondsuit^p_\lambda(U)$) on $\omega$ which form subclasses of Tukey-top ultrafilters, and construct such ultrafilters in $ZFC$. These constructions are
Externí odkaz:
http://arxiv.org/abs/2404.02379
Autor:
Benhamou, Tom
We developed the theory of deterministic ideals and present a systematic study of the pseudo-intersection property with respect to an ideal introduced in \cite{TomNatasha2}. We apply this theory to prove that for any two ultrafilters $U,V$ on $\omega
Externí odkaz:
http://arxiv.org/abs/2312.15261
Autor:
Benhamou, Tom, Zhang, Jing
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 cardi
Externí odkaz:
http://arxiv.org/abs/2307.06910
Autor:
Benhamou, Tom, Goldberg, Gabriel
We continue the study of the Galvin property. In particular, we deepen the connection between certain diamond-like principles and non-Galvin ultrafilters. We also show that any Dodd sound ultrafilter that is not a $p$-point is non-Galvin. We use thes
Externí odkaz:
http://arxiv.org/abs/2306.15078
Autor:
Benhamou, Tom, Dobrinen, Natasha
We develop the theory of cofinal types of ultrafilters over measurable cardinals and establish its connections to Galvin's property. We generalize fundamental results from the countable to the uncountable, but often in surprisingly strengthened forms
Externí odkaz:
http://arxiv.org/abs/2304.07214
We obtain a small ultrafilter number at $\aleph_{\omega_1}$. Moreover, we develop a version of the overlapping strong extender forcing with collapses which can keep the top cardinal $\kappa$ inaccessible. We apply this forcing to construct a model wh
Externí odkaz:
http://arxiv.org/abs/2302.07311
Autor:
Benhamou, Tom
We improve Galvin's Theorem for ultrafilters which are p-point limits of p-points. This implies that in all the canonical inner models up to a superstrong cardinal, every kappa-complete ultrafilter over a measurable cardinal kappa satisfies the Galvi
Externí odkaz:
http://arxiv.org/abs/2212.14096