Related papers: Strongly compct diagonal Prikry forcing
The dynamics of a gravitational torsion kink as a plane symmetric thick domain wall solution of Einstein-Cartan (EC) field equation is given. The spin-torsion energy has to be as high as the gravitational kink potential otherwise torsion…
In these notes, we present an alternative version of discrete Dirac mechanics using Dirac structures. We first establish a notion of 'continuous Dirac system' and then propose a definition of discrete Dirac system, proving that it is…
We introduce the notion of a critical cardinal as the critical point of sufficiently strong elementary embedding between transitive sets. Assuming the axiom of choice this is equivalent to measurability, but it is well-known that choice is…
This dissertation includes many theorems which show how to change large cardinal properties with forcing. I consider in detail the degrees of inaccessible cardinals (an analogue of the classical degrees of Mahlo cardinals) and provide new…
It has been argued recently that diquarks, a pair of quarks in the anti-triplet representation of SU(3) color, are important building blocks of baryons. The assumption that the scalar diquark is tightly bound seems to be nicely accommodated…
A ccc-generically supercompact cardinal $\kappa$ can be smaller than or equal to the continuum. On the other hand, such a cardinal $\kappa$ still satisfies diverse largeness properties, like that it is a stationary limit of ccc-generically…
We analyze a natural function definable from a scale at a singular cardinal, and using this function we are able to obtain quite strong negative square-brackets partition relations at successors of singular cardinals. The proof of our main…
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…
The landmark Levy-Solovay Theorem limits the kind of large cardinal embeddings that can exist in a small forcing extension. Here I announce a generalization of this theorem to a broad new class of forcing notions. One consequence is that…
We study relationships between various set theoretic compactness principles, focusing on the interplay between the three families of combinatorial objects or principles mentioned in the title. Specifically, we show the following. (1) Strong…
Using an extension of Pirogov-Sinai theory we prove phase transitions, corresponding to sublattice orderings, for a general class of hard core lattice particle systems with a finite number of close packed configurations. These include many…
In the context of hard hadronic reactions diquarks are a useful phenomenological device to model non-perturbative effects still observable in the kinematic range accessible by present-day experiments. In the following we present…
We introduce linear Dirac and generalized complex structures on Cartan geometries and give criteria for Dirac subalgebras of $\frkg\ltimes\frkg^*$ representing Dirac structures on a Cartan geometry. We prove that there is a bijection…
We study the nonstationary-support iteration of Prikry forcings below a measurable cardinal \kappa, characterizing all the normal measures it carries in the generic extension. We then analyze the restriction of ultrapower embeddings, taken…
In this paper, we show that the existence of certain first-countable compact-like extensions is equivalent to the equality between corresponding cardinal characteristics of the continuum. For instance, $\mathfrak b=\mathfrak s=\mathfrak c$…
Answering a question of Usuba, we show that an extendible cardinal can be preserved by a set forcing that is not a small forcing.
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…
We investigate fundamental properties of adjoint functors to the precomposition functor in the category of strict polynomial functors.
Simple finite dimensional Kantor triple systems over the complex numbers are classified in terms of Satake diagrams. We prove that every simple and linearly compact Kantor triple system has finite dimension and give an explicit presentation…
In this largely expository paper we give a self-contained treatment of the Dirac operator. Emphasizing the algebraic point of view we first sketch the necessary prerequisites from Clifford algebras and their representations and then define…