Related papers: Compactness in positive logic
Theorems crucial in elementary real function theory have proofs in which compactness arguments are used. Despite the introduction in relatively recent literature of each new highly elegant compactness argument, or of an equivalent, this…
To any finite ordered subset and any finite partition of a group a set of tuples of positive integers, named as configurations, is associated that describes the group's behavior. The present paper provides an exposition of this notion and…
In this paper, we study the properties of closure operators obtained as initial lifts along a reflector, and compactness with respect to them in particular. Applications in the areas of topology, topological groups and topological…
In this paper we will give two different natural generalizations of compact spaces and connected spaces simultaneously. We will show that these generalizations coincide for the subspaces of the real line and that they differ for subspaces…
The construction of first-order logic and set theory gives rise to apparent circularities of mutual dependence, making it unclear which can act as a self-contained starting point in the foundation of mathematics. In this paper, we carry out…
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…
In this paper we discuss contrastive explanations for formal argumentation - the question why a certain argument (the fact) can be accepted, whilst another argument (the foil) cannot be accepted under various extension-based semantics. The…
The first aim of this study is to define soft sequential compact metric spaces and to investigate some important theorems on soft sequential compact metric space. Second is to introduce net and totally bounded soft metric space and study…
We formulate a notion of "punctual gluing" of $t$-structures and weight structures. As our main application we show that the relative version of Ayoub's $1$-motivic $t$-structure restricts to compact motives. We also demonstrate the utility…
We describe a new method for constructing a weight structure $w$ on a triangulated category $C$. For a given $C$ and $w$ it allow us to give a fairly comprehensive (and new) description of those triangulated categories consisting of…
Modelling qualitative uncertainty in formal argumentation is essential both for practical applications and theoretical understanding. Yet, most of the existing works focus on \textit{abstract} models for arguing with uncertainty. Following…
A notion of interpretation between arbitrary logics is introduced, and the poset Log of all logics ordered under interpretability is studied. It is shown that in Log infima of arbitrarily large sets exist, but binary suprema in general do…
We investigate the extent of second order characterizable structures by extending Shelah's Main Gap dichotomy to second order logic. For this end we consider a countable complete first order theory T. We show that all sufficiently large…
Motivated by recent work of Boney, Dimopoulos, Gitman and Magidor, we characterize the existence of weak compactness cardinals for all abstract logics through combinatorial properties of the class of ordinals. This analysis is then used to…
When reasoning in description, modal or temporal logics it is often useful to consider axioms representing universal truths in the domain of discourse. Reasoning with respect to an arbitrary set of axioms is hard, even for relatively…
We introduce the concept of compact quantitative equational theory. A quantitative equational theory is defined to be compact if all its consequences are derivable by means of finite proofs. We prove that the theory of interpolative…
We revise our "Physical Traces" paper in the light of the results in "A Categorical Semantics of Quantum Protocols". The key fact is that the notion of a strongly compact closed category allows abstract notions of adjoint, bipartite…
This is an explanation and defense of "mathematical conceptualism" for a general mathematical and philosophical audience. I make a case that it is cogent, rigorous, attractive, and better suited to ordinary mathematical practice than all…
A category used by de Paiva to model linear logic also occurs in Vojtas's analysis of cardinal characteristics of the continuum. Its morphisms have been used in describing reductions between search problems in complexity theory. We describe…
Motivated by the grid search method and Bayesian optimization, we introduce the concept of contractibility and its applications in model-based optimization. First, a basic framework of contraction methods is established to construct a…