Zobrazeno 1 - 10
of 215
pro vyhledávání: '"03e04"'
Autor:
Levine, Maxwell, Mildenberger, Heike
Cummings, Foreman, and Magidor investigated the extent to which square principles are compact at singular cardinals. The first author proved that if $\kappa$ is a singular strong limit of uncountable cofinality, all scales on $\kappa$ are good, and $
Externí odkaz:
http://arxiv.org/abs/2412.16071
Autor:
Özalp, Tan
Answering a question of Dobrinen and Todorcevic, we prove that below any stable ordered-union ultrafilter $\mathcal{U}$, there are exactly four nonprincipal Tukey classes: $[\mathcal{U}], [\mathcal{U}_{\operatorname{min}}], [\mathcal{U}_{\operatornam
Externí odkaz:
http://arxiv.org/abs/2410.04326
Autor:
Inamdar, Tanmay
We prove that for every colouring of pairs of reals with finitely-many colours, there is a set homeomorphic to the rationals which takes no more than two colours. This was conjectured by Galvin in 1970, and a colouring of Sierpi{\'n}ski from 1933 wit
Externí odkaz:
http://arxiv.org/abs/2405.18431
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:
Gartside, Paul, Morgan, Jeremiah
A directed set $P$ is calibre $(\omega_1, \omega)$ if every uncountable subset of $P$ contains an infinite bounded subset. $P$ is productively calibre $(\omega_1, \omega)$ if $P \times Q$ is calibre $(\omega_1, \omega)$ for every directed set $Q$ wit
Externí odkaz:
http://arxiv.org/abs/2401.02603
Autor:
Feng, Ziqin, Gartside, Paul
Every directed set is Tukey equivalent to (a) the family of all compact subsets, ordered by inclusion, of a (locally compact) space, to (b) a neighborhood filter, ordered by reverse inclusion, of a point (of a compact space, and of a topological grou
Externí odkaz:
http://arxiv.org/abs/2309.06523
Autor:
Matet, Pierre
We deal with values taken by various pseudopower functions at a singular cardinal that is not a fixed point of the aleph function.
Comment: There is a mistake in Proposition 3.4
Comment: There is a mistake in Proposition 3.4
Externí odkaz:
http://arxiv.org/abs/2308.15511
Autor:
Matet, Pierre
Let $\mu < \kappa < \lambda$ be three infinite cardinals, the first two being regular. We show that if there is no inner model with large cardinals, $u (\kappa, \lambda)$ is regular, where $u (\kappa, \lambda)$ denotes the least size of a cofinal sub
Externí odkaz:
http://arxiv.org/abs/2308.14787
Autor:
Matet, Pierre
We revisit the application of Shelah's Revised GCH Theorem \cite{SheRGCH} to diamond. We also formulate a generalization of the theorem and prove a small fragment of it. Finally we consider another application of the theorem, to covering numbers of t
Externí odkaz:
http://arxiv.org/abs/2308.14779