Related papers: Some Remarks on Conway and Iteration Theories
The Isomorphism Conjectures are translated into the language of homotopical algebra, where they resemble Thomason's descent theorems.
In this chapter (Chapter III) we introduce the concept of Conway algebras (the notion related to entropic magmas) and describe invariants of links yielded by (partial) Conway algebras (including the Homflypt polynomial and signatures). We…
We extend the theory of Interacting Hopf algebras with an order primitive, and give a sound and complete axiomatisation of the prop of polyhedral cones. Next, we axiomatise an affine extension and prove soundness and completeness for the…
We give characterizations of unital uniform topological algebras and saturated locally multiplicatively convex algebras by means of multiplicative linear functionals. Some automatic continuity theorems in advertibly complete uniform…
In this monograph, very simple axiomatic definitions to the L. Schwartz' concepts of distribution and derivative of a distribution are formulated. Beyond this, a kind of generalization of that concepts is propose and corresponding axiomatic…
Explaining autonomous and intelligent systems is critical in order to improve trust in their decisions. Counterfactuals have emerged as one of the most compelling forms of explanation. They address ``why not'' questions by revealing how…
Transformation formulas for four-parameter refinements of the q-trinomial coefficients are proven. The iterative nature of these transformations allows for the easy derivation of several infinite series of q-trinomial identities, and can be…
This article represents a major step in the unification of the theory of algebraic, topological and singular transition matrices by introducing a definition which is a generalization that encompasses all of the previous three. When this…
An approach is shown that proves various theorems of plane geometry in an algorithmic manner. The approach affords transparent proofs of a generalization of the Theorem of Morley and other well known results by casting them in terms of…
In this paper we prove that no consistent finitely axiomatized theory one-dimensionally interprets its own extension with predicative comprehension. This constitutes a result with the flavor of the Second Incompleteness Theorem whose…
We present an example of a result in graph theory that is used to obtain a result in another branch of mathematics. More precisely, we show that the isomorphism of certain directed graphs implies that some trinomials over finite fields have…
A rough overview is given over the most essential structures underlying all working quantum theoretical models as well as axiomatic and algebraic quantum field theory .
We develop a general theory of extensions of flat functors along geometric morphisms of toposes, and apply it to the study of the class of theories whose classifying topos is equivalent to a presheaf topos. As a result, we obtain a…
Axiomatic set theory is almost universally accepted as the basic theory which provides the foundations of mathematics, and in which the whole of present day mathematics can be developed. As such, it is the most natural framework for…
In this paper, we use a categorical and functorial set up to model the syntax and inference of logics with algebraic signature, extending previous works on algebraisation of logics. The main feature of this work is that structurality, or…
We develop an extension of institution theory that accommodates implicitly the partiality of the signature morphisms and its syntactic and semantic effects. This is driven primarily by applications to conceptual blending, but other…
We introduce the model-companion of the theory of fields expanded by a unary function for a multiplicative map, which we call ACFH. Among others, we prove that this theory is NSOP$_1$ and not simple, that the kernel of the map is a generic…
The main theorem (2.2) consists in two characterizations of isomorphisms of factorial domains in terms of prime or primary rings elements, and unramified, flat or weakly injective affine schemes morphisms. In order to apply this theorem to…
This note contains some results related to the definitions of toroidal embeddings and toroidal morphisms over non-closed fields of characteristic zero.
We present an axiomatic frame (in Prt I of this book) in which many results of the K-theory for C*-algebras are proved. Then we construct an example for this axiomatic theory (in Part II), which generalizes the classical theory for…