Description of positively existentially closed models in any class of -structures with unary predicates axiomatizable by any h-universal sentence.

Authors

  • A M Kungozhin Al-Farabi Kazakh National University

Abstract

It was shown that any finitely h-universally axiomatized class of models in unary predicate signature has a finite number of positively existentially closed models, and all them are finite. Proposed the example of a class of models which described by the infinite number of h-universal sentences and its class of positively existential closed models is not elementary.

References

[1] Ben Yaacov I., Poizat B., Fondaments de la Logique Positive, The Journal of Symbolic Logic, vol. 82 (2007), pp. 1141-1162.

[2] Kungozhin A. Description of positively existentially closed models in any class of -structures axioma-tizable by the finite number of h-universal sentences with one quantifier, Preprint.

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