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Countable Models of Peano Arithmetic

In: Gödel's Theorems and Zermelo's Axioms

Author

Listed:
  • Lorenz Halbeisen

    (ETH Zurich, Department of Mathematics)

  • Regula Krapf

    (Universität Bonn, Mathematics Institute)

Abstract

By Gödel’s Completeness Theorem 5.5 we know that every consistent theory T has a model. Later we will see that if T has an infinite model, then it also has arbitrarily large models.

Suggested Citation

  • Lorenz Halbeisen & Regula Krapf, 2025. "Countable Models of Peano Arithmetic," Springer Books, in: Gödel's Theorems and Zermelo's Axioms, edition 0, chapter 0, pages 83-89, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-85106-3_8
    DOI: 10.1007/978-3-031-85106-3_8
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