Infinitary Logic: In Memoriam Carol Karp

admissible sets algebraic appear assume atomic formulas automorphisms axioms b₁ back-and-forth basic terms Boolean c₁ cardinality less Carol Karp cf(k chain models cofinality compactness theorem constant symbol COROLLARY countable models define definition disjunctive domain elementarily equivalent elementary submodel elements FAS1 finitary finite finite-quantifier free variables function symbols Hanf number hence implies induction infinitary languages infinitary logic infinite interpolation theorem K-partial Karp Karp's LEMMA Löwenheim-Skolem theorem model existence theorem model of power model theory occurs ordinal P-admissible partially isomorphic predicate proof quantifier recursion theory recursive set relation symbol S₁ S₂ satisfies sequence set theory sets of sentences standard model strict power strong limit cardinal submodels subset Suppose Symbolic Logic t₁ Theorem 4.2 universal valid w₁ well-ordering α α κω