Related papers: Generalized Silver and Miller measurability

We consider global analogues of model-theoretic tree properties. The main objects of study are the invariants related to Shelah's tree property $\kappa_{\text{cdt}}(T)$, $\kappa_{\text{sct}}(T)$, and $\kappa_{\text{inp}}(T)$ and the…

We develop a theory of Lp spaces based on outer measures rather than measures. This theory includes the classical Lp theory on measure spaces as special case. It also covers parts of potential theory and Carleson embedding theorems. The…

We develop a theory of reduction for generalized Kahler and hyper-Kahler structures which uses the generalized Riemannian metric in an essential way, and which is not described with reference solely to a single generalized complex…

We show the existence of a measurable selector in Carpenter's Theorem due to Kadison. This solves a problem posed by Jasper and the first author. As an application we obtain a characterization of all possible spectral functions of…

We answer one of the main questions in generalized descriptive set theory, the Friedman-Hyttinen-Kulikov conjecture on the Borel reducibility of the Main Gap. We show a correlation between Shelah's Main Gap and generalized Borel…

We establish connections between the requirement of measurability of a probability space and the principle of complimentarity in quantum mechanics. It is shown that measurability of a probability space implies the dependence of results of…

We develop a theory of Euler and Kolyvagin systems relative to the Nekov\'{a}\v{r}--Selmer complexes of $p$-adic representations over local complete Gorenstein rings. This theory is both finer and requires fewer hypotheses than those of…

This is a report of a joint work with E. J\"arvenp\"a\"a, M. J\"arvenp\"a\"a, T. Rajala, S. Rogovin, and V. Suomala. In [3], we characterized uniformly porous sets in $s$-regular metric spaces in terms of regular sets by verifying that a…

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…

In this article, the theory of sheaves is studied from a categorical point of view. This perspective vastly generalizes the usual theory of sheaves of sets to a more abstract setting which allows us to investigate the theory of sheaves with…

Generalizing classical descriptive set theory opens foundational questions about the Borel hierarchy. In this paper we systematically study those questions, working in the general framework of Polish-like spaces relative to an uncountable…

We introduce a topology on the space of all isomorphism types represented in a given class of countable models, and use this topology as an aid in classifying the isomorphism types. This mixes ideas from effective descriptive set theory and…

In this article a sequential theory in the category of spaces and proper maps is described and developed. As a natural extension a sequential theory for exterior spaces and maps is obtained.

The aim of this paper is to provide the results that answer the Kuratowski problem posed in 1935 concerning the existence of nonmeasurable sets. The Kuratowski problem was considered for partitions, here we provide a generalization to…

The concept of measurability of functions on a charge space is generalised for functions taking values in a uniform space. Several existing forms of measurability generalise naturally in this context, and new forms of measurability are…

Generalization is at the core of machine learning models. However, the definition of generalization is not entirely clear. We employ set theory to introduce the concepts of algorithms, hypotheses, and dataset generalization. We analyze the…

In this study, we give definition of some multivalued hybrid mappings which are general than many mappings in the existing literature, then we give some existence and convergence results for these mappings in CAT({\kappa})-spaces

An $\mathbb R$-tree is a certain kind of metric space tree in which every point can be branching. Favre and Jonsson posed the following problem in 2004: can the class of orders underlying $\mathbb R$-trees be characterised by the fact that…

In NIP theories, generically stable Keisler measures can be characterized in several ways. We analyze these various forms of "generic stability" in arbitrary theories. Among other things, we show that the standard definition of generic…

We extend the theory of decomposable maps by giving a detailed description of k-positive maps. A relation between transposition and modular theory is established. The structure of positive maps in terms of modular theory (the generalized…