# Mathematical Sciences Research Institute

Home » MT Research Seminar: Existentially closed prime-model extensions of Abelian lattice-ordered groups.

# Seminar

MT Research Seminar: Existentially closed prime-model extensions of Abelian lattice-ordered groups. May 20, 2014 (01:30 PM PDT - 03:00 PM PDT)
Parent Program: Model Theory, Arithmetic Geometry and Number Theory MSRI: Simons Auditorium
Speaker(s) Philip Scowcroft (Wesleyan University)
Description No Description

Video
An Abelian lattice-ordered group--l-group,'' in what follows--is said to be existentially closed (ec) just in case finite systems of l-group equations and inequations over G are solvable in G if solvable in some l-group extending G. An ec prime-model extension of the l-group G is an ec l-group that extends G and embeds over G into every ec l-group extending G. So an l-group G is to an ec prime-model extension of G as a field F is to an algebraic closure of F. This talk will consider the extent to which l-groups have ec prime-model extensions.