Samuel Braunfeld, Michael C. Laskowski
Published 2019-10-24Version 1
We show that if a countable structure $M$ in a finite relational language is not cellular, then there is an age-preserving $N \supseteq M$ such that $2^{\aleph_0}$ many structures are bi-embeddable with $N$. The proof proceeds by a case division based on mutual algebraicity.
Structure and enumeration theorems for hereditary properties in finite relational languages
On omega-categorical structures with few finite substructures
Mutual algebraicity and cellularity
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