Related papers: Pseudo-Prikry sequences
We continue Gitik, Kanovei and Koepke's work and study sets in generic extensions by the Magidor forcing and by the Prikry forcing with non-normal ultrafilters.
In Part I of this series, we introduced a class of notions of forcing which we call Sigma-Prikry, and showed that many of the known Prikry-type notions of forcing that center around singular cardinals of countable cofinality are…
This paper is meant to present in a coherent way several instances of quite common phenomena that was first identified (independently) by Bukovsk\'y and Dehornoy. We present the basic result for Prikry type forcing and show how to extend it…
We examine the existence (and mostly non-existence) of fresh sets in commonly used iterations of Prikry type forcing notions. Results of [4] are generalized. As an application, a question of a referee of [9] is answered. In addition…
Let $D$ be an infinite discrete set of measurable cardinals. It is shown that generalized Prikry forcing to add a countable sequence to each cardinal in $D$ is subcomplete. To do this it is shown that a simplified version of generalized…
It is known that the set of possible cofinalities $\mathrm{pcf}(A)$ has good properties if $A$ is a progressive interval of regular cardinals. In this paper, we give an interval of regular cardinals $A$ such that $\mathrm{pcf}(A)$ has no…
We work with symmetric inner models of forcing extensions based on strongly compact Prikry forcing to extend some known results.
Starting from pseudometrics and preorders on sets of integers, we extend the focus to sets of finite sequences of integers, in particular sequences of consecutive integers. We outline existing concepts for deriving centred pseudometrics and…
I isolate a combinatorial property of a poset $\mathbb{P}$ that I call the strong Prikry property, which implies the existence of an ultrafilter on the complete Boolean algebra $\mathbb{B}$ of $\mathbb{P}$ such that one inclusion of the…
We define a version of Gitik-Sharon diagonal Prikry forcing using a strongly compact cardinal, and prove its basic properties.
We define extender sequences, generelizing measure sequences from Radin Forcing. Using the extender sequences we combine Gitik-Magidor forcing for adding many Prikry sequences with Radin forcing. This forcing satisfies Prikry like…
Some models of combinatorial principles have been obtained by collapsing a huge cardinal in the case of the successors of regular cardinals. For example, saturated ideals, Chang's conjecture, polarized partition relations, and transfer…
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…
In this paper, we study discrete approximations of semi-Dirichlet forms obtained by adding non-symmetric drift terms, expressed in terms of mutual energy measures, to resistance forms whose associated resistance metric spaces are compact.…
Exceptional sequences are certain ordered sequences of quiver representations. We introduce a class of objects called strand diagrams and use this model to classify exceptional sequences of representations of a quiver whose underlying graph…
Distance-regular graphs are a class of regualr graphs with pretty combinatorial symmetry. In 2007, Miklavi\v{c} and Poto\v{c}nik proposed the problem of charaterizing distance-regular Cayley graphs, which can be viewed as a natural…
In this paper, we introduce several classes of Prikry-type forcing notions, two of which are used to produce minimal generic extensions, and the third is applied in $\alpha$-recursion theory to produce minimal covers. The first forcing as a…
Recently the so-called Prabhakar generalization of the fractional Poisson counting process attracted much interest for his flexibility to adapt real world situations. In this renewal process the waiting times between events are IID…
Let $G$ be a connected reductive group over a $p$-adic field $F$ of characteristic 0 and let $M$ be an $F$-Levi subgroup of $G.$ Given a discrete series representation $\sigma$ of $M(F),$ we prove that there exists a locally constant and…
I survey an array of topics in set theory in the context of a novel class of forcing notions: subcomplete forcing. Subcompleteness was originally defined by Ronald Jensen. I have attempted to make the subject somewhat more approachable to…