Related papers: A constructive proof of the phase-type characteriz…
We propose an extension of Aczel's constructive set theory CZF by an axiom for inductive types and a choice principle, and show that this extension has the following properties: it is interpretable in Martin-Lof's type theory (hence…
Kapranov Theorem is a well known generalization of Newton-Puiseux theorem for the case of several variables. This theorem is stated mainly in the context of tropical geometry. We present a new, constructive proof, that also characterizes…
In this note we exhibit a very simple proof of McNaughton Theorem, almost right out of the definitions, and at the same time we observe that this theorem does not depend of Chang's completeness theorem.
Homotopy type theory is a modern foundation for mathematics that introduces the univalence axiom and is particularly suitable for the study of homotopical mathematics and its formalization via proof assistants. In order to better comprehend…
General acceptance of a mathematical proposition $P$ as a theorem requires convincing evidence that a proof of $P$ exists. But what constitutes "convincing evidence?" I will argue that, given the types of evidence that are currently…
We present a unifying framework for type systems for process calculi. The core of the system provides an accurate correspondence between essentially functional processes and linear logic proofs; fragments of this system correspond to…
In this note we give a detailed proof of a theorem of Aubin.
Suppose we have been sold on the idea that formalised proofs in an LCF system should resemble their written counterparts, and so consist of formulas that only provide signposts for a fully verified proof. To be practical, most of the fully…
This article provides a new perspective on the geometry of a projective line, which helps clarify and illuminate some classical results about projective plane. As part of the same train of ideas, the article also provides a proof of the…
A typoid is a type equipped with an equivalence relation, such that the terms of equivalence between the terms of the type satisfy certain conditions, with respect to a given equivalence relation between them, that generalise the properties…
We consider the problem of heterogeneous nucleation and growth. The system is described by a phase field model in which the temperature is included through thermal noise. We show that this phase field approach is suitable to describe…
Discussion of the necessity to use the constructive mathematics as the formalism of quantum theory for systems with many particles.
Pure type systems arise as a generalisation of simply typed lambda calculus. The contemporary development of mathematics has renewed the interest in type theories, as they are not just the object of mere historical research, but have an…
It is well known that the resolution method (for propositional logic) is complete. However, completeness proofs found in the literature use an argument by contradiction showing that if a set of clauses is unsatisfiable, then it must have a…
This is an attempt to create a consistent and non-trivial extension of quantum theory, describing in detail the quantum measurement process. A tentative but concrete model is presented, based on the concept of multiple…
In this paper, we prove a version of the typed B\"ohm theorem on the linear lambda calculus, which says, for any given types A and B, when two different closed terms s1 and s2 of A and any closed terms u1 and u2 of B are given, there is a…
We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…
This paper builds fundamental perfect fields of positive characteristic and shows the structure of perfect fields that a field of positive characteristic is a perfect field if and only if it is an algebraic extension of a fundamental…
Choreographic programming is a paradigm for writing coordination plans for distributed systems from a global point of view, from which correct-by-construction decentralised implementations can be generated automatically. Theory of…
In this short note, we mimic the proof of the simplicity of the theory ACFA of generic difference fields in order to provide a criterion, valid for certain theories of pure fields and fields equipped with operators, which shows that a…