Counting siblings in universal theories

Abstract

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.

26 pages; v3 to appear in Journal of Symbolic Logic

References in corpus (4)

• Uniformly bounded arrays and mutually algebraic structures
• Mutual algebraicity and cellularity
• When does elementary bi-embeddability imply isomorphism?
• Siblings of countable cographs

Cited by in corpus (1)

• Mutual algebraicity and cellularity