The pseudoarc is a co-existentially closed continuum

TL;DR

This paper proves the pseudoarc is a co-existentially closed continuum and shows that the function space C(X) for nondegenerate continua X cannot have quantifier elimination.

Contribution

It establishes the co-existential closure of the pseudoarc and resolves questions about quantifier elimination in C(X) spaces for continua.

Findings

Pseudoarc is co-existentially closed

C(X) cannot have quantifier elimination for nondegenerate continua

Answers to open questions in continuum theory and model theory

Abstract

Answering a question of P. Bankston, we show that the pseudoarc is a co-existentially closed continuum. We also show that $C(X)$, for $X$ a nondegenerate continuum, can never have quantifier elimination, answering a question of the the first and third named authors and Farah and Kirchberg.