indiscernible sequence?
Morley sequence?
Ramsey theorem?
Erdos-Rado theorem?
Ehrenfeucht-Fraïssé games (back-and-forth games)
Hrushovski construction?
generic predicate?
(Birkhoff’s HSP theorem)
Given a language generated by a set of (single-sorted) finitary operations, and a class of structures for . Then is the class of models for a set of universally quantified equations between terms of (a Lawvere theory) if and only if
See also at Lawvere theory – Characterization of examples
Here “closed under homomorphic images” means that if and are structures in the class, and is a homomorphism between them, then also its image is an element of the class.
The first-order analogue of HSP (theorem ) is the characterization (see e.g. Chang and Keisler’s original text (Chang-Keisler 66) on continuous model theory) of elementary classes of structures of structures: they’re precisely those closed under elementary substructures, elementary embeddings, ultraproducts, and ultraroots (if an ultrapower of something is in your class, that something was in your class.)
Wikipedia, Birkhoff's theorem
Chang, Keisler Continuous Model Theory, Princeton University Press, 1966. ISBN: 9780691079295
Last revised on February 24, 2017 at 07:44:15. See the history of this page for a list of all contributions to it.