Submission date: 14 November 2019

Abstract:

We prove two results intended to streamline proofs about cellularity that pass through mutual algebraicity. First, we show that a countable structure M is cellular if and only if M is ω-categorical and mutually algebraic. Second, if a countable structure M in a finite relational language is mutually algebraic non-cellular, we show it admits an elementary extension adding infinitely many infinite MA-connected components.

Mathematics Subject Classification: 03C15

Keywords and phrases:

Full text arXiv 1911.06303: pdf, ps.