Related papers: The Slicing Axioms

We deal with the problem of preserving various versions of completeness in (< kappa) --support iterations of forcing notions, generalizing the case ``S --complete proper is preserved by CS iterations for a stationary co-stationary S…

We investigate a class of actions of real Lie groups on complex spaces. Using moment map techniques we establish the existence of a quotient and a version of Luna's slice theorem as well as a version of the Hilbert-Mumford criterion. A…

We study higher analogues of the classical independence number on $\omega$. For $\kappa$ regular uncountable, we denote by $i(\kappa)$ the minimal size of a maximal $\kappa$-independent family. We establish ZFC relations between $i(\kappa)$…

This paper presents the main results in my Ph.D. thesis. In what follows several proofs of SCH are presented introducing a family of covering properties which implies both SCH and the failure of various forms of square. These covering…

We prove several results giving lower bounds for the large cardinal strength of a failure of the singular cardinal hypothesis. The main result is the following theorem: Theorem: Suppose $\kappa$ is a singular strong limit cardinal and…

Assume $\text{MA}(\kappa)$. We show that for every real chain of size $\kappa$ in the quotient Boolean algebra $P(\omega)/fin$ we can find an almost chain of representatives such that every $n\in\omega$ oscillates at most three times along…

The property of countable metacompactness of a topological space gets its importance from Dowker's 1951 theorem that the product of a normal space X with the unit interval is again normal iff X is countably metacompact. In a recent paper,…

In this paper, we define a class of slice mappings of several Clifford variables, and the corresponding slice regular mappings. Furthermore, we establish the growth theorem for slice regular starlike or convex mappings on the unit ball of…

The axiomatic structure of the $\kappa$-statistcal theory is proven. In addition to the first three standard Khinchin--Shannon axioms of continuity, maximality, and expansibility, two further axioms are identified, namely the self-duality…

This work studies slice functions over finite-dimensional division algebras. Their zero sets are studied in detail along with their multiplicative inverses, for which some unexpected phenomena are discovered. The results are applied to…

We show that the statement ``In every separable pseudometric space there is a maximal non-strictly \delta-separated set.'' implies the axiom of choice for countable families of sets. This gives answers to a question of Dybowski and…

For $n<\omega$, we say that the $\Pi^1_n$-reflection principle holds at $\kappa$ and write $\text{Refl}_n(\kappa)$ if and only if $\kappa$ is a $\Pi^1_n$-indescribable cardinal and every $\Pi^1_n$-indescribable subset of $\kappa$ has a…

We extend the results of Deligne and Illusie on liftings modulo $p^2$ and decompositions of the de Rham complex in several ways. We show that for a smooth scheme $X$ over a perfect field $k$ of characteristic $p>0$, the truncations of the…

We study SLE$_{\kappa}$ theory with elements of Quasi-Sure Stochastic Analysis through Aggregation. Specifically, we show how the latter can be used to construct the SLE$_{\kappa}$ traces quasi-surely (i.e. simultaneously for a family of…

We show that a strong form of the so called Lindstrom's Theorem fails to generalize to extensions of L_{kappa,omega} and L_{kappa,kappa}: For weakly compact kappa there is no strongest extension of L_{kappa,omega} with the…

We study the relationship between two key concepts in the theory of (di)graphs: the quotient digraph, and the lift $\Gamma^{\alpha}$ of a base (voltage) digraph. These techniques contract or expand a given digraph in order to study its…

We present the quantum and classical mechanics formalisms for a particle with position-dependent mass in the context of a deformed algebraic structure (named $\kappa$-algebra), motivated by the Kappa-statistics. From this structure we…

Let chi be the minimum cardinal of a subset of 2^omega that cannot be made convergent by multiplication with a single Toeplitz matrix. By an application of creature forcing we show that s<chi is consistent. We thus answer a question by…

In the original version of this paper, we assume a theory $T$ that the logic $\mathbb L_{\kappa, \aleph_{0}}$ is categorical in a cardinal $\lambda > \kappa$, and $\kappa$ is a measurable cardinal. There we prove that the class of model of…

We look for partition theorems for large subtrees for suitable uncountable trees and colourings. We concentrate on sub-trees of $^{\kappa \ge} 2$ expanded by a well ordering of each level. Unlike earlier works, we do not ask the embedding…