Personal tools
You are here: Home CG seminar 2020 Fusible numbers and Peano Arithmetic
« September 2020 »
September
SuMoTuWeThFrSa
12345
6789101112
13141516171819
20212223242526
27282930
Log in


Forgot your password?
 

Fusible numbers and Peano Arithmetic

Wednesday, June 10th, 2020, 16:10

Checkpoint 480

Zoom: Request the link from Dan Halperin or Golan Levy

underline

Fusible numbers and Peano Arithmetic

Gabriel Nivasch

Abstract:

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.
 
 

Recordings:

Document Actions