Definability and Infinitely Deep Languages

0-absolute 7-structure A-Hintikka Abelian groups absolute relative admissible fragments admissible set admissible structures allows separation analogous arbitrary ARPC Assume atomic formula atomically consistent axiom axiom of choice bijection cardinality w₁ chain of length consider constant symbol continuum hypothesis countable countable vocabulary effective element finite fragment first-order Hintikka sequence Hintikka set implies infinitary infinite cardinal interpolation isomorphic limit chain limit ordinal limit paths locally enumerable logic Loow Löwenheim-Skolem property LS-property M-formula M-languages M-sentence Malitz separation many-sorted languages many-sorted separation mapping metamathematical negated atomic formula negation normal form node obtain obvious one-sorted player predicates and operations proof pseudoformula quantifier regular cardinal relation symbol s-tree semantics sentence separation theorem set theory short Hintikka dialogue sort symbols subformulas subset surjection syntactic label transitive set truth definition unique successor variables well-constructed path well-satisfiable winning strategy