Finite model theory Descriptive complexity theory Model checking Trakhtenbrot's theorem Computable model theory Tarski's exponential function problem Undecidable problem Institutional model theory Institution (computer science) Non-standard analysis Non-standard calculus Hyperinteger Hyperreal number Transfer principle Overspill Elementary Calculus: An Infinitesimal Approach Criticism of non-standard analysis Standard part function Set theory Forcing (mathematics) Boolean-valued model Kripke semantics General frame Predicate logic First-order logic Infinitary logic Many-sorted logic Higher-order logic Lindström quantifier Second-order logic Soundness theorem Gödel's completeness theorem Original proof of Gödel's completeness theorem Compactness theorem Löwenheim–Skolem theorem Skolem's paradox Gödel's incompleteness theorems Structure (mathematical logic) Interpretation (logic) Substructure (mathematics) Elementary substructure Skolem hull Non-standard model Atomic model (mathematical logic) Prime model Saturated model Existentially closed model Ultraproduct Age (model theory) Amalgamation property Hrushovski construction Potential isomorphism Theory (mathematical logic) Complete theory Vaught's test Morley's categoricity theorem Stability spectrum Morley rank Stable theory Forking extension Strongly minimal theory Stable group Tame group o-minimal theory Weakly o-minimal structure C-minimal theory Spectrum of a theory Vaught conjecture Model complete theory List of first-order theories Conservative extension Elementary class Pseudoelementary class Strength (mathematical logic) Differentially closed field Exponential field Ax–Grothendieck theorem Ax–Kochen theorem Peano axioms Non-standard model of arithmetic First-order arithmetic Second-order arithmetic Presburger arithmetic Wilkie's theorem Functional predicate T-schema Back-and-forth method Barwise compactness theorem Skolemization Lindenbaum–Tarski algebra Löb's theorem Arithmetical set Definable set Ehrenfeucht–Fraïssé game Herbrand interpretation / Herbrand structure Imaginary element Indiscernibles Interpretation (model theory) / Interpretable structure Pregeometry (model theory) Quantifier elimination Reduct Signature (logic) Skolem normal form Type (model theory) Zariski geometry