Related papers: Cohesive Powers of Structures
We establish some similarities/analogies between uncountable cardinals or powersets and the class $V$ of all sets. They concern mainly the Boolean algebras ${\cal P}(\kappa)$, for a regular cardinal $\kappa$, and ${\cal C}(V)$ (the class of…
The notion of a complete Boolean algebra, although completely legitimate in constructive mathematics, fails to capture some natural structures such as the lattice of subsets of a given set. Sambin's notion of an overlap algebra, although…
Any single system whose space of states is given by a separable Hilbert space is automatically equipped with infinitely many hidden tensor-like structures. This includes all quantum mechanical systems as well as classical field theories and…
Combinatorics, like computer science, often has to deal with large objects of unspecified (or unusable) structure. One powerful way to deal with such an arbitrary object is to decompose it into more usable components. In particular, it has…
In a 1977 paper, Steffens identified an elegant criterion for determining when a countable graph has a perfect matching. In this paper, we will investigate the proof-theoretic strength of this result and related theorems. We show that a…
Interconnected dynamic systems are a pervasive component of our modern infrastructures. The complexity of such systems can be staggering, which motivates simplified representations for their manipulation and analysis. This work introduces…
A topological monoid is isomorphic to an endomorphism monoid of a countable structure if and only if it is separable and has a compatible complete ultrametric such that composition from the left is non-expansive. We also give a topological…
We study the degrees of selector functions related to the degrees in which a rigid computable structure is relatively computably categorical. It is proved that for some structures such degrees can be represented as the unions of upper cones…
The power graph of a group is the graph whose vertex set is the set of nontrivial elements of group, two elements being adjacent if one is a power of the other. We introduce some way for find the automorphism groups of some graphs. As an…
A binary operation on any set induces a binary operation on its subsets. We explore families of subsets of a group that become a group under the induced operation and refer to such families as power groups of the given group. Our results…
We show that the cohomology table of any coherent sheaf on projective space is a convergent--but possibly infinite--sum of positive real multiples of the cohomology tables of what we call supernatural sheaves.
We study connections between classical asymptotic density and c.e. sets. We prove that a c.e. Turing degree d is not low if and only if d contains a c.e. set A of density 1 which has no computable subsets of density 1, giving a natural…
In this paper, some features of countably $\alpha$-compact topological spaces are presented and proven. The connection between countably $\alpha$% -compact, Tychonoff, and $\alpha$-Hausdorff spaces is explained. The space is countably…
One way of studying a relational structure is to investigate functions which are related to that structure and which leave certain aspects of the structure invariant. Examples are the automorphism group, the self-embedding monoid, the…
The central structure in various versions of noncommutative geometry is a differential calculus on an associative algebra. This is an analogue of the calculus of differential forms on a manifold. In this short review we collect examples of…
A combinatorial characterization of measurable filters on a countable set is found. We apply it to the problem of measurability of the intersection of nonmeasurable filters.
Influence diagram is a graphical representation of belief networks with uncertainty. This article studies the structural properties of a probabilistic model in an influence diagram. In particular, structural controllability theorems and…
A finite number of rational functions are compatible if they satisfy the compatibility conditions of a first-order linear functional system involving differential, shift and q-shift operators. We present a theorem that describes the…
We develop a representation theory of categories as a means to explore characteristic structures in algebra. Characteristic structures play a critical role in isomorphism testing of groups and algebras, and their construction and…
The symmetric tensor power of graphs is introduced and its fundamental properties are explored. A wide range of intriguing phenomena occur when one considers symmetric tensor powers of familiar graphs. A host of open questions are…