Fusible numbers and Peano Arithmetic

Gabriel Nivasch
Ariel University, Israel
http://www.gabrielnivasch.org/home

Date(s) : 14/06/2021   iCal
14 h 00 min - 15 h 00 min

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.

 

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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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