Abstract
We prove a weak version of Fraïssé’s theorem for uncountable classes of finitely generated structures.We also solve Hodges’ problem on failure of the complete analog of this theorem for uncountable classes of finitely generated structures.
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References
C. C. Chang and H. J. Keisler, Model Theory (North-Holland, Amsterdam, 1990).
Yu. L. Ershov, Decision Problems and Constructivizable Models (Nauka, Moscow, 1980) [in Russian].
R. Fraïssé, “Sur l’extension aux relations de quelques propriétés des ordres,” Ann. Sci. École Norm. Sup. (3) 71, 363 (1954) [in French].
W. Hodges, Model Theory (Cambridge Univ. Press, Cambridge, 1993).
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Original Russian Text © K.Zh. Kudaĭbergenov, 2017, published in Matematicheskie Trudy, 2017, Vol. 20, No. 1, pp. 121–127.
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Kudaĭbergenov, K.Z. On Fraïssé’s Theorem for Uncountable Classes of Finitely Generated Structures. Sib. Adv. Math. 28, 60–64 (2018). https://doi.org/10.3103/S1055134418010054
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DOI: https://doi.org/10.3103/S1055134418010054