Existential positive types and preservation under homomorphisms

Published

Conference Paper

We prove the Finite Homomorphism Preservation Theorem: a first-order formula is preserved under homomorphisms 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. © 2005 IEEE.

Duke Authors

Cited Authors

  • Rossman, B

Published Date

  • October 25, 2005

Published In

Start / End Page

  • 467 - 476

International Standard Serial Number (ISSN)

  • 1043-6871

Citation Source

  • Scopus