Thomas Ferguson, University of Amsterdam and University of St. Andrews
Models of relevant arithmetic: Part II
In their technical report “Alien Intruders in Relevant Arithmetic,” Robert Meyer and Chris Mortensen explored models of relevant arithmetic including nonstandard numbers and proved an “Alien Intruder Theorem” that there are models of relevant arithmetic R# in which all rationals exist and act as natural numbers. They observed some “magical” phenomena about these models, like the fact that induction holds of these rational numbers, but did little to explain them. In this talk, I will show how techniques from ultraproduct constructions reveal some of the reasons for these “magical” features, which help demystify some of Meyer and Mortensen’s observations. This is joint work with Elisangela Ramirez at UNAM.