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Quelques précisions sur la D.O.P. et la profondeur d'une théorie

  • D. Lascar (a1)


We give here alternative definitions for the notions that S. Shelah has introduced in recent papers: the dimensional order property and the depth of a theory. We will also give a proof that the depth of a countable theory, when denned, is an ordinal recursive in T.



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[H]Harrison, J., Recursive pseudo-well-orderings, Transactions of the American Mathematical Society, vol. 131 (1968), pp. 526543.
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[L]Lascar, D., Ordre de Rudin-Keisler et poids dans les théories stables, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, vol. 28 (1982), pp. 413430.
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[Sh1]Shelah, S., The lazy model-theoretician's guide to stability, Logique et Analyse, Nouvelle Série, vol. 18 (1975), pp. 241308.
[Sh2]Shelah, S., Classification theory and the number of nonisomorphic models, North-Holland, Amsterdam, 1978.
[Sh3]Shelah, S., The spectrum problem. I, II, Israel Journal of Mathematics, vol. 43 (1982), pp. 324–356, 357364.
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