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Download fileConstructing many atomic models in ℵ1
journal contribution
posted on 2016-12-19, 00:00 authored by JT Baldwin, MC Laskowski, S ShelahWe 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.