Related papers: Lex colimits

Goedel's completeness theorem is concerned with provability, while Girard's theorem in ludics (as well as full completeness theorems in game semantics) are concerned with proofs. Our purpose is to look for a connection between these two…

Given an idempotent complete additive category, we show the there is an explicitly constructed topological space such that the lattice of exact substructures is anti-isomorphic to the lattice of closed subsets. In the special case that the…

The literature on concurrency theory offers a wealth of examples of characteristic-formula constructions for various behavioural relations over finite labelled transition systems and Kripke structures that are defined in terms of fixed…

This paper develops a categorical framework to clarify the relationship between the completeness and compactness theorems in classical first-order logic. Rather than claiming that different model constructions yield naturally isomorphic…

We define a monoid structure on the set of $k$-equal arrangements and use this structure to define limits of braid arrangements. We compute the cohomology of the associated limits of rational models of the arrangements complex complements.…

We show that the category of comodules over a coassociative coalgebra in a complete, cocomplete and well-powered category has limits and colimits under additional assumptions.

In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…

Logical frameworks provide natural and direct ways of specifying and reasoning within deductive systems. The logical framework LF and subsequent developments focus on finitary proof systems, making the formalization of circular proof…

We discuss the problems of incompleteness and inexpressibility. We introduce almost self-referential formulas, use them to extend set theory, and relate their expressive power to that of infinitary logic. We discuss the nature of proper…

For abelian length categories the borderline between finite and infinite representation type is discussed. Characterisations of finite representation type are extended to length categories of infinite height, and the minimal length…

We recover the rays in the tensor product of Hilbert spaces within a larger class of so called `states of compoundness', structured as a complete lattice with the `state of separation' as its top element. At the base of the construction…

We give an answer to the following question: for which metric in an abstract lattice the completion as a metric space coincides with the completion as a lattice. We obtain the answer for inductive limits of lattices which are complete in…

We explain why the naive definition of a natural exact category structure on complete, separated topological vector spaces with linear topology fails. In particular, contrary to arXiv:0711.2527, the category of such topological vector…

We denote by Conc(A) the semilattice of all finitely generated congruences of an (universal) algebra A, and we define Conc(V) as the class of all isomorphic copies of all Conc(A), for A in V, for any variety V of algebras. Let V and W be…

Consistency of case bases is a way to avoid the problem of retrieving conflicting constraining precedents for new cases to be decided. However, in legal practice the consistency requirements for case bases may not be satisfied. As pointed…

The attempt is to give a formal concpet of system, and with this provide a definition of category, that will also satisfy the definition of a system. An axiomatic base is given, for constructing the group of integers. In the process, we…

We give an introduction to constructive category theory by answering two guiding computational questions. The first question is: how do we compute the set of all natural transformations between two finitely presented functors like…

We define the concept of a logic frame, which extends the concept of an abstract logic by adding the concept of a syntax and an axiom system. In a recursive logic frame the syntax and the set of axioms are recursively coded. A recursive…

In Part I of this paper, we introduced a class of certain algebras of finite dimension over a field. All these algebras are split, symmetric and local. Here we continue to investigate their Loewy structure. We show that in many cases their…

It is known that monoidal categories have a finite definition, whereas multicategories have an infinite (albeit finitary) definition. Since monoidal categories correspond to representable multicategories, it goes without saying that…