@article{f97896d5-cbe8-4c08-8b3f-8bee409ef984,
author = {Peter Schuster, Daniel Wessel},
title = {A General Extension Theorem for Directed-Complete Partial Orders},
journal = {Reports on Mathematical Logic},
volume = {2018},
number = {Number 53},
year = {2018},
issn = {0137-2904},
pages = {79-96},keywords = {Extension theorems; Kuratowski-Zornlemma; transfinite methods},
abstract = {The typical indirect proof of an abstract extension theorem, by the Kuratowski-Zorn lemma, is based on a onestep extension argument. While Bell has observed this in case of the axiom of choice, for subfunctions of a given relation, we now consider such extension patterns on arbitrary directed-complete partial orders. By postulating the existence of so-called total elements rather than maximal ones, we can single out an immediate consequence of the Kuratowski-Zorn lemma from which quite a few abstract extension theorems can be deduced more directly, apart from certain definitions by cases. Applications include Baer’s criterion for a module to be injective. Last but not least, our general extension theorem is equivalent to a suitable form of the Kuratowski-Zorn lemma over constructive set theory.},
doi = {10.4467/20842589RM.18.005.8838},
url = {https://ejournals.eu/en/journal/reports-on-mathematical-logic/article/a-general-extension-theorem-for-directed-complete-partial-orders}
}