https://hackerpaper.kaipfister.de/p/2009.09541/Collected HN comments and submissions linking this paper.enMon, 02 Nov 2026 11:16:22 GMThttps://news.ycombinator.com/item?id=38103671urn:hackerpapers:mention:2009.09541:38103671Wed, 01 Nov 2023 19:34:02 GMT<p>Jeremy Avigad made available a 54-page draft chapter on mathematical logic and foundations [1]. Quoting from the abstract: &gt; The formal foundation of a proof assistant is the formal deductive system with respect to which the correctness of the proof assistant’s implementation is judged. The foundation specifies a language for defining objects and saying things about them, and it determines the means that can be used to prove that such statements are true. This chapter presents some general background in logic that is helpful for thinking and reasoning about formal systems, and it describes…</p><p><a href="https://hackerpaper.kaipfister.de/p/2009.09541/">Paper and discussion history</a>. A mention is not an endorsement.</p>cs.LOhttps://news.ycombinator.com/item?id=30819754urn:hackerpapers:mention:2009.09541:30819754Sun, 27 Mar 2022 12:34:11 GMT<p>I agree with you that this is really about the foundations of algebraic topology, but what makes you say that these are not the foundations of mathematics? In the community of computer-aided formalization, a lot of interest in modern type theory arose, because some things in algebraic topology just couldn&#x27;t easily be done in the old First-order-logic + ZFC framework: For example, Kevin Buzzard once asked if Isabelle/HOL (which even uses higher-order-logic) can even be used to formalize schemes! (It turns out that it is possible if you do it in a special way with locales... but the Lean…</p><p><a href="https://hackerpaper.kaipfister.de/p/2009.09541/">Paper and discussion history</a>. A mention is not an endorsement.</p>cs.LO