Constructing many atomic models in ℵ1
View/ Open
Date
2016-09Author
Baldwin, JT
Laskowski, MC
Shelah, S
Publisher
Association for Symbolic LogicMetadata
Show full item recordAbstract
We introduce the notion of pseudo-algebraicity to study atomic models of first
order theories (equivalently models of a complete sentence of Lω1,ω). Theorem: Let
T be any complete first-order theory in a countable language with an atomic model. If
the pseudo-minimal types are not dense, then there are 2
ℵ1 pairwise non-isomorphic
atomic models of T, each of size ℵ1.