• Ieke Moerdijk
  • Jaap van Oosten
Part of the Springer Undergraduate Mathematics Series book series (SUMS)


Formal languages, structures and theories are introduced. Definability issues are presented. The Compactness Theorem is given, with many applications. The compactness is proved using ultrafilters. Elements of model theory are presented: quantifier elimination (as an example: QE for algebraically closed fields, with applications to commutative algebra), elementary substructures, Löwenheim–Skolem theorems and ω-categoricity (back-and-forth method).


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Authors and Affiliations

  • Ieke Moerdijk
    • 1
  • Jaap van Oosten
    • 1
  1. 1.Department of MathematicsUtrecht UniversityUtrechtThe Netherlands

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