Homogeneous and strictly homogeneous criteria for partial structures

  • Authors:

  • Boris A. Romov

  • Affiliations:

  • Bayard Rustin Educational Complex, New York, USA

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2009

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Abstract

The Galois closure on the set of relations invariant to all finite partial automorphisms (automorphisms) of a countable partial structure is established via quantifier-free infinite predicate languages (infinite languages with finite string of quantifiers respectively). Based on it the homogeneous and strictly homogeneous criteria for a countable partial structure as well as an ultrahomogeneous criterion for a countable relational structure are found. Next it is shown that infinite languages with a finite string of quantifiers cannot determine the corresponding Galois closure for relations invariant to all automorphisms of an uncountable partial structure.