Seminar

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.