Related papers: Boolean-valued sets as arbitrary objects
We describe a class calculus that is expressive enough to describe and improve its own learning process. It can design and debug programs that satisfy given input/output constraints, based on its ontology of previously learned programs. It…
Using ideas from synthetic topology, a new approach to descriptive set theory is suggested. Synthetic descriptive set theory promises elegant explanations for various phenomena in both classic and effective descriptive set theory.…
Tree sets are abstract structures that can be used to model various tree-shaped objects in combinatorics. Finite tree sets can be represented by finite graph-theoretical trees. We extend this representation theory to infinite tree sets.…
We study the concept of universal sets from the additive--combinatorial point of view. Among other results we obtain some applications of this type of uniformity to sets avoiding solutions to linear equations, and get an optimal upper bound…
The author's attempt to construct a local causal model of quantum theory (QT) that includes quantum field theory (QFT) resulted in the identification of "quantum objects" as the elementary units of causality and locality. Quantum objects…
Recent advances in string theory and inflationary cosmology have led to a surge of interest in the possible existence of an ensemble of cosmic regions, or universes, among the members of which key physical parameters, such as the masses of…
In problems such as variable selection and graph estimation, models are characterized by Boolean logical structure such as presence or absence of a variable or an edge. Consequently, false positive error or false negative error can be…
Let $G$ be a polycyclic, metabelian or soluble of type (FP)$_{\infty}$ group such that the class $Rat(G)$ of all rational subsets of $G$ is a boolean algebra. Then $G$ is virtually abelian. Every soluble biautomatic group is virtually…
This is an overview of the recent results of interaction of Boolean valued analysis and vector lattice theory.
Questions of set-theoretic size play an essential role in category theory, especially the distinction between sets and proper classes (or small sets and large sets). There are many different ways to formalize this, and which choice is made…
In this paper we characterize the projective modules over an arbitrary quantale, and then we apply such a characterization in order to define the K_0 group of a quantale. Then we study congruences of quantales and quantale modules by means…
We study links between first-order formulas and arbitrary properties for families of theories, classes of structures and their isomorphism types. Possibilities for ranks and degrees for formulas and theories with respect to given properties…
We study languages over infinite alphabets equipped with some structure that can be tested by recognizing automata. We develop a framework for studying such alphabets and the ensuing automata theory, where the key role is played by an…
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…
We investigate an extension of ZFC set theory (in an extended language) that stipulates the existence of a proper class of indiscernibles over the universe. One of the main results of the paper shows that the purely set-theoretical…
In fairly elementary terms this paper presents how the theory of preordered fuzzy sets, more precisely quantale-valued preorders on quantale-valued fuzzy sets, is established under the guidance of enriched category theory. Motivated by…
We develop a theory of formal multivariate polynomials over commutative rings by treating them as ring terms. Our main result is that two ring terms are s-equivalent (when expanded they yield the same standard polynomial) iff they are…
Tame abstract elementary classes are a broad nonelementary framework for model theory that encompasses several examples of interest. In recent years, progress toward developing a classification theory for them have been made. Abstract…
We formulate a theory of shape valid for objects of arbitrary dimension whose contours are path connected. We apply this theory to the design and modeling of viable trajectories of complex dynamical systems. Infinite families of…
We show that the closure of the value set of a real linear recurrence sequence is the union of a countable set and a finite collection of intervals. Conversely, any finite collection of closed intervals is the closure of the value set of…