Provability, Computability and Reflection

argument assume assumption axioms binary relation Chapter construction contains contradiction Corollary countable Counterexample defined definition denote Dom(f Dom(g downward Löwenheim–Skolem theorem element elementary enumeration equivalent example exists extended filter finite formula q free variables full cardinal sums function symbol Hanf number hence implies incompact increasing sequence individual constant induction hypothesis infinitary languages infinite cardinal isomorphism k-complete large cardinality Lemma Let Q limit ordinal linear orderings Lºx map f measurable cardinal model theory non-principal notation obtain omitting order type ordered set partial isomorphisms preceding proof of Theorem prove quantifiers Range(f relation symbol REMARK result satisfies set of indiscernibles similarity type Skolem Skolem functions strongly compact strongly compact cardinal strongly inaccessible cardinal structure QI structures of type subset substructure successor ordinal transitive set ultrafilter ultraproduct unary well-ordered whence