Related papers: Continuous integration logic
Positive logic is a generalisation of full first-order logic that does not have negation built in. Still, many model-theoretic ideas, tools and techniques work perfectly fine in positive logic. Importantly, there is a compactness theorem.…
The tight span, or injective envelope, is an elegant and useful construction that takes a metric space and returns the smallest hyperconvex space into which it can be embedded. The concept has stimulated a large body of theory and has…
Within the framework of balayage spaces (the analytical equivalent of nice Hunt processes), we prove equicontinuity of bounded families of harmonic functions and apply it to obtain criteria for compactness of potential kernels.
A variety of problems emerged investigating electronic circuits, computer devices and cellular automata motivated a number of attempts to create a differential and integral calculus for Boolean functions. In the present article, we extend…
We study extensions of the measure of maximal entropy to suitable compactifications of the parameter space and the moduli space of rational maps acting on the Riemann sphere. For parameter space, we consider a space which resolves the…
We take a unifying and new approach toward polynomial and trigonometric approximation in an arbitrary number of variables, resulting in a precise and general ready-to-use tool that anyone can easily apply in new situations of interest. The…
We extend the theoretical framework of proof mining by establishing general logical metatheorems that allow for the extraction of the computational content of theorems with prima facie "non-computational" proofs from probability theory,…
We prove that if $X$ is a topological space that admits Debreu's classical utility theorem (eg.\ $X$ is separable and connected, second countable, etc.), then order relations on $X$ satisfying milder completeness conditions can be…
We prove analogues of the Craig interpolation theorem for the continuous model theory of metric structures.
We present a logical framework for formalizing connections between finitary combinatorics and measure theory or ergodic theory that have appeared various places throughout the literature. We develop the basic syntax and semantics of this…
In this paper we have introduced arithmetic ff-continuity and arithmetic fb-continuity utilizing the concept of forward and backward arithmetic convergence in quasi cone metric spaces. These concepts are used to prove some fascinating…
In this paper (propositional) probability logic ($PL$) is investigated from model theoretic point of view. First of all, the ultraproduct construction is adapted for $\sigma$-additive probability models, and subsequently when this class of…
We prove, in ZFC alone, some new results on regularity and decomposability of ultrafilters. We also list some problems, and furnish applications to topological spaces and to extended logics.
In this paper, we study several propositional team logics that are closed under unions, including propositional inclusion logic. We prove that all these logics are expressively complete, and we introduce sound and complete systems of…
Within the framework of computable infinitary continuous logic, we develop a system of hyperarithmetic numerals. These numerals are infinitary sentences in a metric language $L$ that have the same truth value in every interpretation of $L$.…
In this thesis, the main objects of study are probability measures on the isomorphism classes of countable, connected rooted graphs. An important class of such measures is formed by unimodular measures, which satisfy a certain equation,…
We describe some Cartesian products of metric spaces and find conditions under which products of ultrametric spaces are ultrametric.
We define a strongly normalising proof-net calculus corresponding to the logic of strongly compact closed categories with biproducts. The calculus is a full and faithful representation of the free strongly compact closed category with…
Motivated by partition regularity problems of homogeneous quadratic equations, we prove multiple recurrence and convergence results for multiplicative measure preserving actions with iterates given by rational sequences involving…
We construct a De Morgan algebra-valued logic with quantifiers, where the truth values are in a finite De Morgan algebra, We show that there is a representation theorem of the cylindric algebra of this logic from which a completeness…