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Vol. 5(5), 2005 (Section Logic)
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Some Results on Ordered Structures in Toposes
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Luís A. Sbardellini
Personal web-page
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Date Posted: May, 30th 2005
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.Abstract
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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.
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