A Sheaf Model of the Algebraic Closure
Logic
2014-09-12 v4
Abstract
In constructive algebra one cannot in general decide the irreducibility of a polynomial over a field K. This poses some problems to showing the existence of the algebraic closure of K. We give a possible constructive interpretation of the existence of the algebraic closure of a field in characteristic 0 by building, in a constructive metatheory, a suitable site model where there is such an algebraic closure. One can then extract computational content from this model. We give examples of computation based on this model.
Cite
@article{arxiv.1404.4549,
title = {A Sheaf Model of the Algebraic Closure},
author = {Bassel Mannaa and Thierry Coquand},
journal= {arXiv preprint arXiv:1404.4549},
year = {2014}
}
Comments
In Proceedings CL&C 2014, arXiv:1409.2593