Related papers: Stone type representation theorems via games

It has been shown that a functional interpretation of proofs in mathematical analysis can be given by the product of selection functions, a mode of recursion that has an intuitive reading in terms of the computation of optimal strategies in…

For finitary regular monads T on locally finitely presentable categories we characterize the finitely presentable objects in the category of T-algebras in the style known from general algebra: they are precisely the algebras presentable by…

We present a game semantics for intuitionistic type theory. Specifically, we propose categories with families of a new variant of games and strategies for both extensional and intensional variants of the type theory with dependent function,…

We construct representation theory of Lie algebras with filtrations. In this framework a classification of irreducible representations is obtained and spectra of some reducible representations are found.

We show that the class of representable substitution algebras is characterized by a set of universal first order sentences. In addition, it is shown that a necessary and sufficient condition for a substitution algebra to be representable is…

A partial algebra construction of Gr\"atzer and Schmidt from "Characterizations of congruence lattices of abstract algebras" (Acta Sci. Math. (Szeged) 24 (1963), 34-59) is adapted to provide an alternative proof to a well-known fact that…

Axioms are presented which encapsulate the properties satisfied by categories of games which form the basis of results on full abstraction for PCF and other programming languages, and on full completeness for various logics and type…

Reynolds' parametricity originally equips types with proof-irrelevant binary propositional relations over the types. But such relations can also be taken proof-relevant or unary, and described either in an indexed or fibred way.…

We propose in this paper a polynomial representation of TU-games, fuzzy measures, capacities, and more generally set functions. Our representation needs a countably infinite set of players and the natural ordering of finite sets of…

A simple and general formulation of the quantum game theory is presented, accommodating all possible strategies in the Hilbert space for the first time. The theory is solvable for the two strategy quantum game, which is shown to be…

We introduce the notions of weakly *-concave and weakly naturally quasi-concave correspondence and prove fixed point theorems and continuous selection theorems for these kind of correspondences. As applications in the game theory, by using…

We reduce the set of classic relational algebra operators to two binary operations: natural join and generalized union. We further demonstrate that this set of operators is relationally complete and honors lattice axioms.

Axiomatizing mathematical structures and theories is an objective of Mathematical Logic. Some axiomatic systems are nowadays mere definitions, such as the axioms of Group Theory; but some systems are much deeper, such as the axioms of…

We show that the common theory of all modules over a tubular algebra (over a recursive algebraically closed field) is decidable. This result supports a long standing conjecture of Mike Prest which says that a finite-dimensional algebra…

An algebraic theory, sometimes called an equational theory, is a theory defined by finitary operations and equations, such as the theories of groups and of rings. It is well known that algebraic theories are equivalent to finitary monads on…

Binary relations are one of the standard ways to encode, characterise and reason about graphs. Relation algebras provide equational axioms for a large fragment of the calculus of binary relations. Although relations are standard tools in…

Relative property (T) has recently been used to construct a variety of new rigidity phenomena, for example in von Neumann algebras and the study of orbit-equivalence relations. However, until recently there were few examples of group pairs…

We present vector-lattice-theoretic proofs of Riesz Representation Theorem and Stone Representation Theorem.

For an ascending correspondence $F:X\to 2^X$ with chain-complete values on a complete lattice $X$, we prove that the set of fixed points is a complete lattice. This strengthens Zhou's fixed point theorem. For chain-complete posets that are…

A new technique for proving fixed point theorems for families of holomorphic transformations of operator balls is developed. One of these theorems is used to show that a bounded representation in a real or complex Hilbert space is…