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arXiv · 2509.09623

Extending orders to types

Lorenzo Luperi Baglini·Marcello Mamino·Rosario Mennuni·Mariaclara Ragosta·Boris Šobot
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Abstract

Given an ordered structure, we study a natural way to extend the order to preorders on type spaces. For definably complete, linearly ordered structures, we give a characterisation of the preorder on the space of 1-types. We apply these results to the divisibility preorder on the space of ultrafilters on the set of natural numbers, giving an independence result about the suborder consisting of ultrafilters with only one fixed prime divisor, as well as a classification of ultrafilters with finitely many prime divisors.

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Lorenzo Luperi Baglini, Marcello Mamino, Rosario Mennuni, Mariaclara Ragosta, Boris Šobot. 2025-09-11. Extending orders to types. https://doi.org/10.60866/cam.297

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