Keywords
K-finite objects
decidable objects
Teoría de topos
objetos K-finitos
objetos decidibles
How to Cite
Abstract
In an elemetary topos ε, we prove that the class of K-finite decidable objects is the same to the class of finite cardinals in E if and only if every K-finite decidable object X such that X → 1 is epic, then 1→ X is split epic.
References
Acuña-Ortega, O. (1986) “An exact coexact characterization of the finite cardinals”, Journal of Pure and Applied Algebra 43(3): 211–233.
Acuña-Ortega, O. (1977) Finiteness in Topoi, Ph. D. Dissertation, Wesleyan University, Middletown, CT.
Acuña-Ortega, O. (1986) “Sobre una definición de cardinales funitos en un topos arbitrario”, Revista Colombiana de Matemáticas 20(3–4):
Acuña-Ortega, O.; Linton, F.E.J. (1979) “Finiteness and decidability I”, in: Applications of Sheaves, Lecture Notes in Mathematics 753, Springer–Verlag, New York: 80–100.
Benabou, J. (s.f.) “Definability, finiteness, projectivity and choice”, (preliminary version), to appear.