Post #1961211

www.paultaylor.eu/trans/ "Old and New Proofs of the Order-Theoretic Fixed Point Theorem" I have just posted a new version of this paper (which was advertised here on 30 December by Toucanlan). It was motivated primarily by my irritation with so-called proofs that recite stuff about successor and limit ordinals and conclude fixed points. Missing are what ordinal to use and the derivation of recursion from induction. It gives the complete proof of this using transfinite recursion, quoting the original papers by Cantor, Hartogs and von Neumann. I have never found this in the literature. It also gives the proof of the so-called Bourbaki-Witt theorem, actually due to Zermelo and Kuratowski. ("Zorn's Lemma" and "Tarski's Theorem" are also claerly stated in Kuratowski's 1922 paper.) But as well there is the shorter, simpler constructive proof by Pataraia and me. Plus a lot of history, which is a rabbit-hole! I welcome comments from people who know the actual mathematical history (1904--23), not the post-war mythology.