Lovely pairs of models: the non first order case

Itaï Ben Yaacov (1)

1 MIT Math Dept

We prove that for every simple theory $T$ (or even simple thick compact abstract theory) there is a (unique) compact abstract theory $T^\fP$ whose saturated models are the lovely pairs of $T$. Independence-theoretic results that were proved in [Ben Yaacov, Pillay, Vassiliev - Lovely pairs of models] when $T^\fP$ is a first order theory are proved for the general case: in particular $T^\fP$ is simple and we characterise independence.

Mots clés: simple theories; lovely pairs

Domaines: Logique [math.LO]

Itaï Ben Yaacov. Lovely pairs of models: the non first order case. The Journal of Symbolic Logic, 2004, 69 (3), pp.641-662. ⟨hal-00357704⟩