相关论文: On Some Properties of Shelah Cardinals
In this paper we review Shelah's strong covering property and its applications. We also extend some of the results of Shelah and Woodin on the failure of $CH$ by adding a real.
We show that Shelah cardinals are preserved under the canonical $GCH$ forcing notion. We also show that if $GCH$ holds and $F:REG\rightarrow CARD$ is an Easton function which satisfies some weak properties, then there exists a cofinality…
In this note, we relax the hypothesis of the main results in Kellner-Shelah-T\v{a}nasie's "Another ordering of the ten cardinal characteristics in Cicho\'n's diagram".
In the paper, the authors find some integral representations and discover some properties of Lah numbers.
In this paper, we study a special type of ultrafilter which we call Shelah ultrafilter. We show that it is possible to add a Shelah ultrafilter using a special forcing notion. We also show that Shelah ultrafilters turn out to be…
In this note we provide some applications of L\"owenheim-Skolem cardinals introduced in \cite{U}.
We show that some cardinal arithmetic configurations related to the negation of the Shelah Weak Hypothesis and natural from the forcing point of view are impossible.
The article uses two examples to explore the statement that, contrary to the common wisdom, the properties of singular cardinals are actually more intuitive than those of the regular ones.
We formulate and prove (in {\sf ZFC}) a strong coloring theorem which holds at successors of singular cardinals, and use it to answer several questions concerning Shelah's principle $Pr_1(\mu^+,\mu^+,\mu^+,\cf(\mu))$ for singular $\mu$.
Using GCH, we force the following: There are continuum many simple cardinal characteristics with pairwise different values.
A property of a filter, a kind of large cardinal property, suffices for the proof in Liu Shelah [LiSh:484] and is proved consistent as required there. A natural property which looks better, not only is not obtained here, but is shown to be…
We introduce and axiomatize the notion of a reflective cardinal, use it to give semantics to higher order set theory, and explore connections between the notion of reflective cardinals and large cardinal axioms.
We consider some of the various formulations of the Revised GCH Theorem presented in Shelah's original paper \cite{SheRGCH}. We compare them and discuss their meaning.
This brief survey comes from the slides of a seminar I gave to philosophy of mathematics students. I will present some different characterizations of Woodin cardinals, including the one obtained by Ernest Schimmerling in [6]. I will try to…
We characterize the situation of having many normal measures on a measurable cardinal. We show the plausibility of having many normal measures on each compact cardinal.
In [Bon20], model theoretic characterizations of several established large cardinal notions were given. We continue this work, by establishing such characterizations for Woodin cardinals (and variants), various virtual large cardinals, and…
We study the consistency and consistency strength of various configurations concerning the cardinal characteristics $\mathfrak{s}_\theta,\mathfrak{p}_\theta,\mathfrak{g}_\theta,\mathfrak{r}_\theta,\mathfrak{t}_\theta$ at uncountable regular…
We give full characterization of the sequences of regular cardinals that may arise as cardinal sequences of locally compact scattered spaces under GCH. The proofs are based on constructions of universal locally compact scattered spaces.
We give some lower bounds on the Shelah rank of varieties in the free group whose coordinate groups are hyperbolic towers.
We show that Shelah's Eventual Categoricity Conjecture follows from the existence of class many strongly compact cardinals. This is the first time the consistency of this conjecture has been proven. We do so by showing that every AEC with…