Passages between finite and infinite.

When Can Finite Testing Ensure Infinite Trustworthiness?

In this paper we contribute to the general philosophical‎ ‎question as to whether empirical testing can ever prove a physical law.‎ ‎Problems that lead to this question arise under several contexts‎, ‎and the ‎matter has been addressed by the likes of Bayes and Laplace‎. ‎After pointing‎ ‎out that a Bayesian approach is the proper way to address this problem‎, ‎we‎ ‎show that the answ...

Some Connections between Finite and Infinite Model Theory

Most of the work in model theory has, so far, considered infinite structures and the methods and results that have been worked out in this context can usually not be transferred to the study of finite structures in any obvious way; in addition, some basic results from infinite model theory fail within the context of finite models. The theory about finite structures has largely developed in conn...

Complementation: a bridge between finite and infinite proofs

When a proposition has no proof in an inference system, it is sometimes useful to build a counter-proof explaining, step by step, the reason of this non-provability. In general, this counter-proof is a (possibly) infinite co-inductive proof in a different inference system. In this paper, we show that, for some decidable inference systems, this (possibly) infinite proof has a representation as a...

Some Connections between Finite and Infinite Model Theory

Finite and Infinite Packings

Let K E d , d 2, be a centrally symmetric convex body with volume V (K) > 0 and distance function f. be the density of a densest packing of n translates of K, where controls the innuence of the boundary. We show that for 2 lim sup n!1 where (K) is the classical densest innnite packing density of K. So we get a new approach to classical packings. For d = 2 we generalize classical results by Roge...