Constructive foundations of potential theory

Constructive Foundations for Z

The speciication language Z is based on classical logic and extensional set theory. These are mathematical choices which are largely independent of Z and its calculus of schemata. This paper explores the possibilities of replacing classical logic with intuitionistic logic and extensional set theory with intensional set theory, and some of the consequences of these changes for principles of prog...

Foundations of Euclidean Constructive Geometry

Euclidean geometry, as presented by Euclid, consists of straightedge-andcompass constructions and rigorous reasoning about the results of those constructions. A consideration of the relation of the Euclidean “constructions” to “constructive mathematics” leads to the development of a first-order theory ECG of “Euclidean Constructive Geometry”, which can serve as an axiomatization of Euclid rathe...

Constructive Foundations for Featherweight Java

In this paper we present a recursion-theoretic denotational semantics for Featherweight Java. Our interpretation is based on a formalization of the object model of Castagna, Ghelli and Longo in a predicative theory of types and names. Although this theory is prooftheoretically weak, it allows to prove many properties of programs written in Featherweight Java. This underpins Feferman’s thesis th...

On the Foundations of a Constructive Theory of Discrete Commutative Algebra.

Constructive Function Theory on Sets of the Complex Plane through Potential Theory and Geometric Function Theory

This is a survey of some recent results concerning polynomial inequalities and polynomial approximation of functions in the complex plane. The results are achieved by the application of methods and techniques of modern geometric function theory and potential theory. MSC: 30C10, 30C15, 41A10