nLab
Galois type

Idea

Galois types are a generalization of types for abstract elementary classes with amalgamation property.

Consider the type (in model theory) tp(a/M)tp(a/M) for a first order theory in larger uncountable saturated model MM' (of cardinality strictly larger than of the underlying language). By a standard result it can be identified with the orbit of aa under the automorphism group Aut M(M)Aut_M(M') of MM' fixing MM pointwise. This is taken as a definition for some infinitary theories in the case we have the monster model. A slightly weaker version can be rephrased in terms of amalgamation.

Definition

Let (K,<)(K,\lt) be an abstract elementary class of structures.

References

  • Rami Grossberg, Classification theory for abstract elementary classes (section 6), Logic and Algebra, ed. Yi Zhang, Contemporary Mathematics 302, AMS, (2002) 165–204, pdf
  • Rami Grossberg, Monica VanDieren, Galois-stability for tame abstract elementary classes, Journal of Mathematical Logic 6, No. 1 (2006) 25–49, pdf
Revised on August 4, 2012 14:52:12 by Zoran Škoda (95.168.113.34)