Linear extension: Difference between revisions

Revision as of 07:54, 1 February 2014

Revision as of 06:28, 6 September 2014

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| year = 1930}}.</ref>

In modern [[axiomatic set theory]] the order-extension theoryprinciple 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

| last = Jech | first = Thomas | author-link = Thomas Jech

| isbn = 0-486-46624-8

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| publisher = [[Dover Publications]]

| title = The Axiom of Choice

| year = 2008}}.</ref> but the reverse implication isdoesn't not provablehold.<ref>{{citation

| last1 = Felgner | first1 = U.

| last2 = Truss | first2 = J. K.