Some Results on Ordered Structures in Toposes

Abstract. A topos version of Cantor's back and forth theorem is established and used to prove that the ordered structure of the rational numbers Q, < is homogeneous in any topos with natural numbers object. The notion of effective homogeneity is introduced, and it is shown that Q, < is a minimal effectively homogeneous structure, that is, it can be embedded in every other effectively homogeneous ordered structure.

• Type: Journal
• Year: 2006
• Where: RML
• Authors: Luís A. Sbardellini, Marcelo E. Coniglio
• Keywords: Business, Natural Numbers, Rational Numbers, RML 2006, Topos Version