Existential Positive Types and Preservation under Homomorphisisms

  • Authors:

  • Benjamin Rossman

  • Affiliations:

  • -

  • Venue:
  • LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
  • Year:
  • 2005

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Abstract

We prove the Finite Homomorphism Preservation Theorem: a first-order formula is preserved underhomomorphisms on finite structures iff it is equivalent in the finite to an existential positive formula. We also strengthen the classical homomorphism preservation theorem by showing that a formula is preserved under homomorphisms on all structures iff it is equivalent to an existential positive formula of the same quantifier rank. Our method involves analysis of existential positive types and a new notion of existential positive saturation.