✦ LIBER ✦

The ascending chain condition for real ideas

✍ Scribed by Paulo Ribenboim

Book ID: 105104637
Publisher: Springer
Year: 1986
Tongue: English
Weight: 504 KB
Volume: 57
Category: Article
ISSN: 0025-2611
DOI: 10.1007/bf01172494

No coin nor oath required. For personal study only.

📜 SIMILAR VOLUMES

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A Remark on Ascending Chain Conditions, the Countable Axiom of Choice and the Principle of Dependent Choices

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## Abstract It is easy to prove in ZF^−^ (= Zermelo‐Fraenkel set theory without the axioms of choice and foundation) that a relation __R__ satisfies the maximal condition if and only if its transitive hull __R__\* does; equivalently: __R__ is well‐founded if and only if __R__\* is. We will show in