We prove a structure theorem asserting that each superflat graph is tree-decomposable in a very nice way. As a consequence we fully determine the spectrum functions of theories of superflat graphs.
Institute of Mathematics, Wrocław University, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
Bibliografia
[1] J. T. Baldwin, Fundamentals of Stability Theory, Springer, New York, 1985.
[2] J. T. Baldwin and S. Shelah, Second-order quantifiers and the complexity of theories, Notre Dame J. Formal Logic 26 (1985), 229-303.
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[8] E. A. Palyutin and S. S. Starchenko, Horn theories with non-maximal spectra, in: Model Theory and its Applications, Yu. L. Ershov (ed.), Nauka, Novosibirsk, 1988, 108-161.
[9] A. Pillay, Simple superstable theories, in: Classification Theory, J. T. Baldwin (ed.), Lecture Notes in Math. 1292, Springer, Heidelberg, 1987, 247-263.
[10] K. Podewski and M. Ziegler, Stable graphs, Fund. Math. 100 (1978), 101-107.
[11] A. N. Ryaskin, The number of models of complete theories of unars, in: Model Theory and its Applications, Yu. L. Ershov (ed.), Nauka, Novosibirsk, 1988, 162-182 (in Russian).
[12] J. Saffe, The number of uncountable models of ω-stable theories, Ann. Pure Appl. Logic 24 (1983), 231-261.
[13] S. Shelah, Classification Theory and the Number of Non-Isomorphic Models, North-Holland, Amsterdam, 1978.
[14] S. Shelah, On almost categorical theories, in: Classification Theory, J. T. Baldwin (ed.), Lecture Notes in Math. 1292, Springer, Heidelberg, 1987, 498-500.