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Mathematics > Logic
Title: Chain Bounding and the leanest proof of Zorn's lemma
(Submitted on 17 Apr 2024)
Abstract: We present an exposition of the *Chain Bounding Lemma*, which is a common generalization of both Zorn's Lemma and the Bourbaki-Witt fixed point theorem. The proofs of these results through the use of Chain Bounding are amongst the simplest ones that we are aware of. As a by-product, we show that for every poset $P$ and a function $f$ from the powerset of $P$ into $P$, there exists a maximal well-ordered chain whose family of initial segments is appropriately closed under $f$.
We also provide a "computer formalization" of our main results using the Lean proof assistant.
Submission history
From: Pedro Sánchez Terraf [view email][v1] Wed, 17 Apr 2024 16:19:16 GMT (15kb)
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