相关论文: Even more simple cardinal invariants

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…

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.

Under large cardinal hypotheses beyond the Kunen inconsistency -- hypotheses so strong as to contradict the Axiom of Choice -- we solve several variants of the generalized continuum problem and identify structural features of the levels…

We construct a variety of inner models exhibiting features usually obtained by forcing over universes with large cardinals. For example, if there is a supercompact cardinal, then there is an inner model with a Laver indestructible…

We introduce poly-Cauchy permutations that are enumerated by the poly-Cauchy numbers. We provide combinatorial proofs for several identities involving poly-Cauchy numbers and some of their generalizations. The aim of this work is to…

We summarize the known methods of producing a non-supercompact strongly compact cardinal and describe some new variants. Our Main Theorem shows how to apply these methods to many cardinals simultaneously and exactly control which cardinals…

We reimplement the creature forcing construction used by Fischer et al. (arXiv:1402.0367) to separate Cicho\'{n}'s diagram into five cardinals as a countable support product. Using the fact that it is of countable support, we augment our…

Combining creature forcing approaches from arXiv:1003.3425 and arXiv:1402.0367, we show that, under CH, there is a proper $\omega^\omega$-bounding poset with $\aleph_2$-cc that forces continuum many pairwise different cardinal…

There is a set of continual cardinality of pairwise disjoint Gaussian automorphisms with spectrally isomorphic even factors having Lebesgue spectrum.

We show that many large cardinal notions up to measurability can be characterized through the existence of certain filters for small models of set theory. This correspondence will allow us to obtain a canonical way in which to assign ideals…

We consider natural cardinal invariants hm_n and prove several duality theorems, saying roughly: if I is a suitably definable ideal and provably cov(I)>=hm_n, then non(I) is provably small. The proofs integrate the determinacy theory,…

We prove that the strong polarized relation for the continuum holds for $\aleph_0$ and for every supercompact cardinal. We use iteration of Mathias forcing.

We deal with relatives of GCH which are provable. In particular we deal with rank version of the revised GCH. Our motivation was to find such results when only weak versions of the axiom of choice are assumed but some of the results gives…

Reflection principles (or dually speaking, compactness principles) often give rise to combinatorial guessing principles. Uniformization properties, on the other hand, are examples of anti-guessing principles. We discuss the tension and the…

The results of the previous version are impoved. This basically completes the study of consistency strength of various gaps between a strong limit singular cardinal of cofinality omega and its power under GCH type assumptions below.

We show that supercompactness and strong compactness can be equivalent even as properties of pairs of regular cardinals. Specifically, we show that if V models ZFC + GCH is a given model (which in interesting cases contains instances of…

We introduce a two-parameter modification of the cofinality invariant of ideals. This allows us to include the interaction of a pair of ideals in the study of base-like structures. We find the values (cardinal numbers or well-known cardinal…

For $\kappa$ regular and uncountable we define variants of the classical cardinal characteristics modulo the non-stationary ideal.

We list some open problems, concerning the polarized partition relation. We solve a couple of them by showing that for every singular cardinal $\mu$ one can force the strong polarized relation with respect to the pair $\mu^+,\mu$.

We show: There are pairs of universes V_1 subseteq V_2 and there is a notion of forcing P in V_1 such that the change mentioned in the title occurs when going from V_1[G] to V_2[G] for a P-generic filter G over V_2. We use forcing…