Coherent and finiteness spaces

TL;DR

This paper introduces a functorial relationship between coherent spaces and finiteness spaces in linear logic, utilizing the infinite Ramsey theorem, and explores the cardinality of finiteness spaces on N.

Contribution

It establishes a new functor from coherent spaces to finiteness spaces that preserves linear logic structures, using the infinite Ramsey theorem for conceptual insight.

Findings

A functor from COH to FIN commuting with linear logic operations

The use of the infinite Ramsey theorem in this context

Cardinality results for finiteness spaces on N

Abstract

This short note presents a new relation between coherent spaces and finiteness spaces. This takes the form of a functor from COH to FIN commuting with the additive and multiplicative structure of linear logic. What makes this correspondence possible and conceptually interesting is the use of the infinite Ramsey theorem. Along the way, the question of the cardinality of the collection of finiteness spaces on N is answered. Basic knowledge about coherent spaces and finiteness spaces is assumed.