Topological models of arithmetic
Tom 256 / 2022
Fundamenta Mathematicae 256 (2022), 171-193
MSC: Primary 03C62; Secondary 03C66.
DOI: 10.4064/fm928-1-2021
Opublikowany online: 10 May 2021
Streszczenie
Ali Enayat had asked whether there is a model of PA (Peano Arithmetic) that can be represented as , where \oplus and \otimes are continuous functions on the rationals \mathbb Q . We prove, affirmatively, that indeed every countable model of PA has such a continuous presentation on the rationals. More generally, we investigate the topological spaces that arise as such topological models of arithmetic. Finite-dimensional Euclidean spaces \mathbb R ^n and compact Hausdorff spaces do not, and neither does any Suslin line; many other spaces do. The status of the space of irrationals remains open.
