= Homogeneous model
A model is strongly $\kappa$-homogeneous when every <partial elementary map> between its subsets of size less than $\kappa$ extends to an <automorphism>. Here the unqualified expression <homogeneous model> uses this automorphism extension convention. For finite parameter tuples it says, in particular, that equal <complete types> can be carried to one another by an <automorphism>.
A weaker local convention asks only for one-point extensions of small <partial elementary maps>. A $\kappa$-<saturated model> always has that local property. If its cardinality is $\kappa$, the <back-and-forth method> yields the strong version too. For example, order-preserving maps between finite subsets of the rational <dense linear order without endpoints> extend to automorphisms by back-and-forth.
Back to article page
