Fusible numbers and Peano Arithmetic
Gabriel Nivasch
Ariel University, Israel
http://www.gabrielnivasch.org/home
Date(s) : 14/06/2021 iCal
14h00 - 15h00
Inspired by a mathematical riddle involving fuses, we define a set of rational numbers which we call « fusible numbers ». We prove that the set of fusible numbers is well-ordered in R, with order type eps_0. We prove that the density of the fusible numbers along the real line grows at an incredibly fast rate, namely at least like the function F_{eps_0} of the fast-growing hierarchy. Finally, we derive some true statements that can be formulated but not proven in Peano Arithmetic, of a different flavor than previously known such statements, for example, « For every natural number n there exists a smallest fusible number larger than n. » Joint work with Jeff Erickson and Junyan Xu. https://arxiv.org/abs/2003.14342
We will also briefly mention some recent progress on generalizations of fusible numbers, joint work with Alexander Bufetov and Fedor Pakhomov.
Lecture room link: https://bbb1.cirm-math.fr/b/org-n9z-3je
Access code: see mail
Joint seminar of SIMC and HSE by A. I. Bufetov, A. V. Dymov, A. V. Klimenko, M. Mariani and G. I. Olshanskii “Representations and Probability”
June 14, 2021 15:00–16:20, Moscow, online via BigBlueButton. To get the link, write to klimenko@mi-ras.ru
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