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FROM A1 TO D5: TOWARDS A FORCING-RELATED CLASSIFICATION OF RELATIONAL STRUCTURES

  • MILOŠ S. KURILIĆ (a1)

Abstract

We investigate the partial orderings of the form P(X),⊂〉, where X is a relational structure and P(X) the set of the domains of its isomorphic substructures. A rough classification of countable binary structures corresponding to the forcing-related properties of the posets of their copies is obtained.

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[1] Kechris, A. S., Classical descriptive set theory, Graduate Texts in Mathematics, vol. 156, Springer-Verlag, New York, 1995.
[2] Kunen, K., Set theory. An introduction to independence proofs, Studies in Logic and the Foundations of Mathematics, vol. 102, North-Holland, Amsterdam, New York, 1980.
[3] Kurilić, M. S. and Todorčevi&cacute, S., Forcing by non-scattered sets. Annals of Pure and Applied Logic, vol. 163 (2012), pp. 12991308.
[4] Kurili&cacute, M. S., Maximally embeddable components. Archive for Mathematical Logic, vol. 52 (2013), no. 7, pp. 793808.
[5] Kurili&cacute, M. S., Posets of copies of countable scattered linear orders. Annals of Pure and Applied Logic, vol. 165 (2014), pp. 895912.
[6] Kurili&cacute, M. S., Forcing with copies of countable ordinals. Proceedings of the American Mathematical Society, (to appear).
[7] Kurili&cacute, M. S., Embedding-minimal structures, submitted.
[8] Pouzet, M., Relations impartibles, Dissertationes Mathematicae (Rozprawy Matematyczne), vol. 193 (1981).
[9] Shelah, S. and Spinas, O., The distributivity numbers of P(w)/ fin and its square. Transactions of the American Mathematical Society, vol. 352 (2000), no. 5, pp. 20232047.
[10] Talagrand, M., Compacts de fonctions mesurables et filtres non mesurables. Studia Mathematica, vol. 67 (1980), no. 1, pp. 1343.

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FROM A1 TO D5: TOWARDS A FORCING-RELATED CLASSIFICATION OF RELATIONAL STRUCTURES

  • MILOŠ S. KURILIĆ (a1)

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