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