Documentation

InfinitaryLogic.ModelTheory.SmallModels

Small models: public facade #

The stable entry point for the small-model theorem (Marker, Lectures on Infinitary Model Theory, Theorem 11.2). Importing this file (or the default import InfinitaryLogic) exposes:

The proof route (issue #11): the schema term source of the Morley seed (the morley_hanf machinery) over a highly order-transitive skeleton of size κ (every linear ordered field is highly order-transitive; Hahn-series subfields realize every infinite cardinality); the local EM quotient is equivariant under order automorphisms of the skeleton, so tuples are classified up to automorphism by countably many compressed term codes; located term codes give the exact carrier cardinality; and the arbitrary-language wrapper is a reduct along the uniform collapsing hom, so smallness descends generically.