Open Collections

Description

A field K is called pseudo-algebraically closed (PAC) if every absolutely irreducible variety defined over K has a K-rational point. These fields were introduced by Ax in his characterization of pseudo-finite fields and have since become an important object of model-theoretic study. A remarkable theorem of Chatzidakis proves that, in a precise sense, independent amalgamation in a PAC field is controlled by independent amalgamation in the absolute Galois group. We will describe how this theorem and a graph-coding construction of Cherlin, van den Dries, and Macintyre may be combined to construct PAC fields with prescribed model-theoretic properties.