Geodesic
Countably categorical theories
Algebra i logika, Tome 51 (2012) no. 3, pp. 358-384.

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A series of countably categorical theories are constructed based on the Fraisse method. In particular, an example of a decidable countably categorical theory of finite signature is given for which no decidable model has an infinite computable set of order-indiscernible elements. Such a theory is used to refute Ershov's conjecture on the representability of models of $c$-simple theories over linear orders.
Keywords: countably categorical theory, decidable theory, decidable model, linear order.
Mots-clés : Fraisse method 
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V. G. Puzarenko. Countably categorical theories. Algebra i logika, Tome 51 (2012) no. 3, pp. 358-384. http://geodesic.mathdoc.fr/item/AL_2012_51_3_a4/

[1] Yu. L. Ershov, “$\Sigma$-definability of algebraic systems”, Handbook of recursive mathematics, v. 1, Stud. Logic Found. Math., 138, Recursive model theory, eds. Yu. L. Ershov et al., Elsevier, Amsterdam, 1998, 235–260 | DOI | MR | Zbl

[2] Yu. L. Ershov, V. G. Puzarenko, A. I. Stukachev, “$\mathbb{HF}$-Computability”, Computability in context. Computation and logic in the real world, eds. S. B. Cooper, A. Sorbi, World Scientific, London, 2011, 169–242 | DOI | MR | Zbl

[3] W. Hodges, Model theory, Encycl. Math. Appl., 42, Cambridge Univ. Press, Cambridge, 1993 | MR | Zbl

[4] S. S. Goncharov, Yu. L. Ershov, Konstruktivnye modeli, Sibirskaya shkola algebry i logiki, Nauchnaya kniga, Novosibirsk, 1999

[5] B. F. Csima, V. S. Harizanov, R. Miller, A. Montalban, “Computability of Fraïsse limits”, J. Symb. Log., 76:1 (2011), 66–93 | DOI | MR | Zbl

[6] H. A. Kierstead, J. B. Remmel, “Indiscernibles and decidable models”, J. Symb. Log., 48:1 (1983), 21–32 | DOI | MR | Zbl

[7] V. G. Puzarenko, “Obobschennye numeratsii i opredelimost polya $\mathbb R$ v dopustimykh mnozhestvakh”, Vestnik NGU. Ser. matem., mekh., inform., 3:2 (2003), 107–117

[8] Yu. L. Ershov, Opredelimost i vychislimost, Sibirskaya shkola algebry i logiki, Nauchnaya kniga (NII MIOO NGU), Novosibirsk, 1996 | MR | Zbl

[9] V. G. Puzarenko, “O razreshimykh vychislimykh $\mathbb A$-numeratsiyakh”, Algebra i logika, 41:5 (2002), 568–584 | MR | Zbl

[10] A. I. Stukachev, “$\Sigma$-opredelimost v nasledstvenno konechnykh nadstroikakh i pary modelei”, Algebra i logika, 43:4 (2004), 459–481 | MR | Zbl