List of Mathematical Logic Topics - Model Theory

Model Theory

  • 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
  • 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 / Herbrand universe
  • Imaginary element
  • Indiscernibles
  • Interpretation (model theory) / Interpretable structure
  • Pregeometry (model theory)
  • Quantifier elimination
  • Reduct
  • Signature (logic)
  • Skolem normal form
  • Type (model theory)
  • Zariski geometry

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