Kurt Gödel Research Center

2017 seminar talk: Some properties of Cohen and random reals

Talk held by Mohammad Golshani (Institute for Research in Fundamental Sciences (IPM), Tehran, Iran) at the KGRC seminar on 2017-10-05.

Abstract

We discuss some properties of Cohen and random reals. We prove a general combinatorial fact about them which in particular implies that they are large, they contain arbitrary large arithmetical or geometrical progressions, satisfy the Hindman's conclusion and so on. We also show that they are wild in the sense of o‑minimal theory. We also investigate how badly approximable are they by algebraic numbers.

This is a work in progress with Will Brian.