Provability, Computability and Reflection

admissible set assume atomic formula axiom cardinal Compactness Theorem complete formula consistency property constant symbols COROLLARY countable fragment countable model countable set countably many types defined elementary chain elementary embedding elementary submodel elements end elementary extension end extension finitely many c e follows fragment of Lolo free variables Hanf number Hence holds hypothesis infinitary logic infinite set isomorphic k-categorical Lebesgue measure lecture LEMMA Let Q limit ordinal Loio Lola Lºy Model Existence Theorem model of power model of ZF model Qſ model theory Molo MORLEY n-tuple Omitting Types Theorem order logic power o1 proof of Theorem prove QI F realizes recursively relation symbol set of indiscernibles set of sentences Skolem functions ſº submodel subset Suppose Theorem 28 Theorem 30 transitive e-model ultrapower ultraproducts uncountable model well-orderable whence Zermelo set theory