×

Semi-isolation and the strict order property. (English) Zbl 1372.03058

Summary: We study semi-isolation as a binary relation on the locus of a complete type and prove that – under some additional assumptions – it induces the strict order property.

MSC:

03C15 Model theory of denumerable and separable structures
03C45 Classification theory, stability, and related concepts in model theory
PDFBibTeX XMLCite
Full Text: DOI arXiv Euclid

References:

[1] Baizhanov, B. S., S. V. Sudoplatov, and V. V. Verbovskiy, “Conditions for non-symmetric relations of semi-isolation,” Siberian Electronic Mathematical Reports , vol. 9 (2012), pp. 161-84. · Zbl 1330.03073
[2] Benda, M., “Remarks on countable models,” Fundamenta Mathematicae , vol. 81 (1973/74), pp. 107-19. · Zbl 0289.02038
[3] Ikeda, K., A. Pillay, and A. Tsuboi, “On theories having three countable models,” Mathematical Logic Quarterly , vol. 44 (1998), pp. 161-66. · Zbl 0897.03035 · doi:10.1002/malq.19980440203
[4] Peretjat’kin, M. G., “Complete theories with a finite number of countable models” (in Russian), Algebra i Logika , vol. 12 (1973), pp. 550-76; English translation in Algebra and Logic , vol. 12 (1973), pp. 310-26.
[5] Pillay, A., “Instability and theories with few models,” Proceedings of the American Mathematical Society , vol. 80 (1980), pp. 461-68. · Zbl 0034.00801 · doi:10.2307/2266510
[6] Saffe, J., E. A. Palyutin, and S. S. Starchenko, “Models of superstable Horn theories” (in Russian), Algebra i Logika , vol. 24 (1985), pp. 278-326; English translation in Algebra and Logic , vol. 24 (1985), pp. 171-210. · Zbl 0597.03017 · doi:10.1007/BF02080332
[7] Sudoplatov, S. V., “Powerful types in small theories,” Siberian Mathematical Journal , vol. 31 (1990), pp. 629-38. · Zbl 0723.03018 · doi:10.1007/BF00970635
[8] Sudoplatov, S. V., The Lachlan Problem (in Russian), Edition of Novosibirsk State Technical University, Novosibirsk, Russia, 2009.
[9] Tanović, P., “Theories with constants and three countable models,” Archive for Mathematical Logic , vol. 46 (2007), pp. 517-27. · Zbl 1115.03026 · doi:10.1007/s00153-007-0054-2
[10] Tanović, P., “Asymmetric RK-minimal types,” Archive for Mathematical Logic , vol. 49 (2010), pp. 367-77. · Zbl 1241.03045 · doi:10.1090/S0002-9947-2011-05382-1
[11] Vaught, R. L., “Denumerable models of complete theories,” pp. 303-21 in Infinitistic Methods (Warsaw, 1959) , Pergamon, Oxford, 1961. · Zbl 0113.24302
[12] Woodrow, R. E., “A note on countable complete theories having three isomorphism types of countable models,” Journal of Symbolic Logic , vol. 41 (1976), pp. 672-80. · Zbl 0373.02036 · doi:10.2307/2272044
[13] Woodrow, R. E., “Theories with a finite number of countable models,” Journal of Symbolic Logic , vol. 43 (1978), pp. 442-55. · Zbl 0434.03022 · doi:10.2307/2273520
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.