https://hackerpaper.kaipfister.de/p/2009.04980/Collected HN comments and submissions linking this paper.enMon, 02 Nov 2026 11:16:22 GMThttps://news.ycombinator.com/item?id=38062871urn:hackerpapers:mention:2009.04980:38062871Sun, 29 Oct 2023 21:13:27 GMT<p>You write, &quot;we shouldn&#x27;t need the axiom of choice to define the derivative.&quot; The good news is that we don&#x27;t! Only model-theoretic approaches, which justify the infinitesimal methods by constructing a hyperreal field, require (a weak form of) the axiom of choice [2]. However, there are axioms for nonstandard analysis which are conservative over the usual choice-free set theory ZF. The three axioms of Hrbacek and Katz presented in the article &quot;Infinitesimal analysis without the Axiom of Choice&quot; [1] are the best recent example: these axioms allow you to do everything that is done in Keisler&#x27;s…</p><p><a href="https://hackerpaper.kaipfister.de/p/2009.04980/">Paper and discussion history</a>. A mention is not an endorsement.</p>math.LO