Related papers: Regularity Properties on the Generalized Reals
We introduce general regular variation, a theory of regular variation containing the existing Karamata, Bojanic-Karamata/de Haan and Beurling theories as special cases. The unifying theme is the Popa groups of our title viewed as locally…
We provide a comprehensive development of the basics of descriptive set theory for non-separable complete metric spaces whose weight is a singular cardinal $\lambda$ of countable confinality. Somewhat unexpectedly, the resulting theory is…
We prove a revised version of Laver's indestructibility theorem which slightly improves over the classical result. An application yields the consistency of $(\kappa^+,\kappa)\notcc(\aleph\_1,\aleph\_0)$ when $\kappa$ is supercompact. The…
A duality of $\kappa$-normed topological vector spaces is defined and investigated. For such spaces the analog of the Mackey-Arens theorem is proved. There are investigated cases, when $\kappa$-normability of a topological vector space…
This paper investigates the problem of extending measure theory to non-separable structures, from generalized descriptive set theory to a broader class of spaces beyond this framework. While various notions, such as the ideal of measure…
The kappa-deformed statistics has been studied in many papers. It is naturally important question for us to ask what should the kappa parameter stand for and under what physical situation should the kappa-deformed statistics be suitable for…
Kunen's proof of the non-existence of Reinhardt cardinals opened up the research on very large cardinals, i.e., hypotheses at the limit of inconsistency. One of these large cardinals, I0, proved to have descriptive-set-theoretical…
If $\kappa$ is regular and $2^{<\kappa}\leq\kappa^+$, then the existence of a weakly presaturated ideal on $\kappa^+$ implies $\square^*_\kappa$. This partially answers a question of Foreman and Magidor about the approachability ideal on…
Building on early work by Stevo Todorcevic, we describe a theory of stationary subtrees of trees of successor-cardinal height. We define the diagonal union of subsets of a tree, as well as normal ideals on a tree, and we characterize…
We present the main features of the mathematical theory generated by the \kappa-deformed exponential function exp_{\kappa}(x)=(\sqrt{1+\kappa^2 x^2}+\kappa x)^{1/\kappa}, with 0<\kappa<1, developed in the last twelve years, which turns out…
W.H. Woodin showed that if $\kappa_1 < \cdots < \kappa_n$ are strong cardinals then two-step ${\bf\Sigma}^1_{n+3}$ generic absoluteness holds after collapsing $2^{2^{\kappa_n}}$ to be countable. We show that this number can be reduced to…
Let $\kappa$ be an infinite cardinal. Then, forcing with $\mathbb{R}(\kappa)$$\times$$\mathbb{R}(\kappa)$ adds a generic filter for $\mathbb{C}(\kappa);$ where $\mathbb{R}(\kappa)$ and $\mathbb{C}(\kappa)$ are the forcing notions for adding…
Assuming the existence of a proper class of supercompact cardinals, we force that for every regular cardinal $\kappa$, there are $\kappa^+$-Aronszajn trees and all such trees are special.
We show that higher Sacks forcing at a regular limit cardinal and club Miller forcing at an uncountable regular cardinal both add a diamond sequence. We answer the longstanding question, whether $\kappa = \kappa^{<\kappa} \geq\aleph_1$…
We discuss the effect of adding a single real (for various forcing notions adding reals) on cardinal invariants associated with the continuum (like the unbounding or the dominating number or the cardinals related to measure and category on…
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…
For a regular uncountable cardinal kappa, we discuss the order relationship between the unbounding and dominating numbers on kappa and cardinal invariants of the higher meager ideal M_kappa. In particular, we obtain a complete…
The theory of the $\kappa$-deformed Poincare algebra is applied to the analysis of various phenomena in special relativity, quantum mechanics and field theory. The method relies on the development of series expansions in $\kappa^{-1}$ of…
We establish radiative stability of generalized Proca effective field theories. While standard powercounting arguments would conclude otherwise, we find non-trivial cancellations of leading order corrections by explicit computation of…
This paper provides two characterizations of regularity for near-vector spaces: first, by expressing them as a direct sum of vector spaces over division rings formed by distributive elements; second, by expressing their dimension in term of…