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:
infinitaryType/RealizedInfinitaryTypes/Lomega1omegaSmall— the complete-type API (ModelTheory/InfinitaryTypes.lean);exists_small_model_of_hasArbLargeModels— a sentence with arbitrarily large models has, at every infiniteκ, a model of size exactlyκrealizing only countably many completeL_{ω₁ω}-types — over an arbitrary language;exists_small_model_of_hasArbLargeModels_countable_symbols— the transparent countable-symbol core.
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.