Related papers: Mouse Sets
In this paper, using definability of types over indiscernible sequences as a template, we study a property of formulas and theories called "uniform definability of types over finite sets" (UDTFS). We explore UDTFS and show how it relates to…
In this paper we show that if $(X,\mathcal{A})$ is a measurable space and if $Y$ is a topological model of a Lawvere theory $\mathcal{T}$ equipped with $\mathcal{B}$ the Borel $\sigma$-algebra on $Y$, then the set of…
We consider the covering of a ball in certain normed spaces by its congruent subsets and show that if the finite number of sets is not greater than the dimensionality of the space, then the centre of the ball either belongs to the interior…
In this paper we consider nonmeasurablity with respect to sigma-ideals defined be trees. First classical example of such ideal is Marczewski ideal s_0. We will consider also ideal l_0 defined by Laver trees and m_0 defined by Miller trees.…
We introduce the notion of an M-family of infinite subsets of $\nn$ which is implicitly contained in the work of A. R. D. Mathias. We study the structure of a pair of orthogonal hereditary families $\aaa$ and $\bbb$, where $\aaa$ is…
Soft set theory can deal uncertainties in nature by parametrization process. In this paper, we explore the objects and morphisms of category of soft sets, Sset(U) in detail. Also, gives characterizations of monomorphisms and epimorphisms in…
We develop the theory of meta-iteration trees, that is, iteration trees whose base "model" is itself an ordinary iteration tree. We prove a comparison theorem for meta-iteration strategies parallel to the one for ordinary iteration…
At present, practical application and theoretical discussion of rough sets are two hot problems in computer science. The core concepts of rough set theory are upper and lower approximation operators based on equivalence relations. Matroid,…
This paper clarifies the picture about Dense-choice Counter Machines, which have been less studied than (discrete) Counter Machines. We revisit the definition of "Dense Counter Machines" so that it now extends (discrete) Counter Machines,…
Machine learning-based techniques open up many opportunities and improvements to derive deeper and more practical insights from data that can help businesses make informed decisions. However, the majority of these techniques focus on the…
Open Set Recognition (OSR) is about dealing with unknown situations that were not learned by the models during training. In this paper, we provide a survey of existing works about OSR and distinguish their respective advantages and…
Algebraic theories with dependency between sorts form the structural core of Martin-L\"of type theory and similar systems. Their denotational semantics are typically studied using categorical techniques; many different categorical…
A random set is a generalisation of a random variable, i.e. a set-valued random variable. The random set theory allows a unification of other uncertainty descriptions such as interval variable, mass belief function in Dempster-Shafer theory…
We define a generalization of the Turing machine that computes on general sets. Our main theorem states that the class of generalized Turing machine computable functions and the class of Set Recursive functions coincide.
It is true in the Cohen generic extension of L, the constructible universe, that every countable ordinal-definable set of reals belongs to L.
Regular model checking is an exploration technique for infinite state systems where state spaces are represented as regular languages and transition relations are expressed using rational relations over infinite (or finite) strings. We…
In this paper, a new kind of soft sets related with some common decision making problems in real life called central soft sets is introduced. Properties of some basic operations on central soft sets are shown. It is investigated that some…
The arrow relation, a central concept in extremal set theory, captures quantitative relationships between families of sets and their traces. Formally, the arrow relation $(n, m) \rightarrow (a, b)$ signifies that for any family $\mathcal{F}…
We consider a set-theoretic version of mereology based on the inclusion relation $\subseteq$ and analyze how well it might serve as a foundation of mathematics. After establishing the non-definability of $\in$ from $\subseteq$, we identify…
An $n\times n$ matrix $M$ is called a \textit{fooling-set matrix of size $n$} if its diagonal entries are nonzero and $M_{k,\ell} M_{\ell,k} = 0$ for every $k\ne \ell$. Dietzfelbinger, Hromkovi{\v{c}}, and Schnitger (1996) showed that $n…