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| url = http://matwbn.icm.edu.pl/ksiazki/fm/fm16/fm16125.pdf
| volume = 16
| year = 1930| doi = 10.4064/fm-16-1-386-389 | doi-access = free
}}.</ref> In modern [[axiomatic set theory]] the order-extension principle is itself taken as an axiom, of comparable ontological status to the axiom of choice. The order-extension principle is implied by the [[Boolean prime ideal theorem]] or the equivalent [[compactness theorem]],<ref>{{citation
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