Finitary Extensions

  • J. Donald Monk
Part of the Graduate Texts in Mathematics book series (GTM, volume 37)


In this chapter we want to consider various essential extensions of first-order languages in which the formulas are still of finite length. In particular, we shall consider higher-order logic, ω-logic, and cardinality quantifiers.


Prefix Decid 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bell, J. L. and Slomson, A. B. Models and Ultraproducts. Amsterdam: North-Holland (1969).MATHGoogle Scholar
  2. 2.
    Henkin, L. Completeness in the theory of types. J. Symb. Logic, 15 (1950), 81–91.MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Keisler, H. J. Some model-theoretic results for ω-logic. Israel J. Math., 4 (1966), 249–261.MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Läuchli, H. A decision procedure for the weak second-order theory of linear order. In Contrib. math. logic. Amsterdam: North-Holland (1968), 189–197.Google Scholar
  5. 5.
    Mostowski, A. On a generalization of quantifiers. Fund. Math., 44 (1957), 12–36.MathSciNetGoogle Scholar
  6. 6.
    Rabin, M. Decidability of second-order theories and automata on infinite trees. Trans. Amer. Math. Soc., 141 (1969), 1–35.MathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag Inc. 1976

Authors and Affiliations

  • J. Donald Monk
    • 1
  1. 1.Department of MathematicsUniversity of ColoradoBoulderUSA

Personalised recommendations