BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Sam Sanders (Ruhr-Universität Bochum) DTSTART:20230831T180000Z DTEND:20230831T190000Z DTSTAMP:20260423T021248Z UID:OLS/140 DESCRIPTION:Title: Th e Biggest Five of Reverse Mathematics\nby Sam Sanders (Ruhr-Universit ät Bochum) as part of Online logic seminar\n\n\nAbstract\nI provide an ov erview of joint work with Dag Normann on the higher-order Reverse Mathemat ics (RM for short) of the Big Five systems and the surprising limits of th is enterprise ([3]).\n\nThe well-known Big Five phenomenon of RM is the ob servation that a large number of theorems from ordinary mathematics are ei ther provable in the base theory or equivalent to one of only four systems \; these five systems together are called the ‘Big Five’ of RM. The ai m of this paper is to greatly extend the Big Five phenomenon\, working in Kohlenbach’s higher-order RM ([1]).\n\nIn particular\, we have establish ed numerous equivalences involving the second-order Big Five systems on on e hand\, and well-known third-order theorems from analysis about (possibly ) discontinuous functions on the other hand. We both study relatively tame notions\, like cadlag or Baire 1\, and potentially wild ones\, like quasi -continuity. We also show that slight generalisations and variations (invo lving e.g. the notions Baire 2 and cliquishness) of the aforementioned thi rd-order theorems fall far outside of the Big Five. In particular\, these slight generalisations and variations imply the principle NIN from [2]\, i .e. there is no injection from [0\, 1] to N. We discuss a possible explana tion for this phenomenon.\n\nREFERENCES.\n\n[1] Ulrich Kohlenbach\, Higher order reverse mathematics\, Reverse mathematics 2001\, Lect. Notes Log.\, vol. 21\, ASL\, 2005\, pp. 281–295.\n\n[2] Dag Normann and Sam Sanders\ , On the uncountability of R\, Journal of Symbolic Logic\, DOI: doi.org/ 1 0.1017/jsl.2022.27 (2022)\, pp. 43.\n\n[3] _________________________\, The Biggest Five of Reverse Mathematics\, Submitted\, arxiv: https://arxiv.or g/abs/2212.00489 (2023)\, pp. 39.\n LOCATION:https://researchseminars.org/talk/OLS/140/ END:VEVENT END:VCALENDAR