2014/04/30 by Bassel Mannaa, Thierry Coquand
Mathematics · #math.LO
paper · pdf · doi:10.4204/eptcs.164.2
published as EPTCS 164, 2014, pp. 18-32 · In Proceedings CL&C 2014, arXiv:1409.2593
arxiv created 2014/09/11 · arxiv updated 2014/09/12
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.