Valuation theory: A constructive view

A Constructive Valuation Semantics for ClassicalLogicFranco

The paper presents a constructive interpretation for proofs in classical logic of 0 1 sentences and for a witness extraction procedure based on Prawitz's reduction rules.

A Constructive View of Complete Regularity

Apartness, Topology, and Uniformity: a Constructive View

The theory of apartness spaces, and their relation to topological spaces (in the point—set case) and uniform spaces (in the set—set case), is sketched. New notions of local decomposability and regularity are investigated, and the latter is used to produce an example of a classically metrisable apartness on R that cannot be induced constructively by even a uniform structure.

A constructive view on ergodic theorems

Let T be a positive L1-L∞ contraction. We prove that the following statements are equivalent in constructive mathematics. 1. The projection in L2 on the space N : = cl{x−T x: x∈L2} exists; 2. The sequence (T n)n∈N Cesàro-converges in the L2 norm; 3. The sequence (T n)n∈N Cesàro-converges almost everywhere. Thus, we find necessary and sufficient conditions for the Mean Ergodic Theorem and the Du...

Constructive Matrix Theory

We extend the technique of constructive expansions to compute the connected functions of matrix models in a uniform way as the size of the matrix increases. This provides the main missing ingredient for a non-perturbative construction of the φ 4 field theory on the Moyal four dimensional space.