Homogeneous and strictly homogeneous criteria for partial structures |
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Authors: | Boris A Romov |
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Institution: | Bayard Rustin Educational Complex, New York, USA |
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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. |
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Keywords: | Galois closure Partial structure Language with finite string of quantifiers Homogeneous structure |
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