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Sibirskii Matematicheskii Zhurnal, 2011, Volume 52, Number 2, Pages 393–399 (Mi smj2205)  
Existence of saturated structures

V. G. Puzarenkoab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
b Novosibirsk State University, Mechanics and Mathematics Department, Novosibirsk, Russia
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Abstract: Under discussion in this paper are real closed fields saturated enough. We give an example of a structure on which all arithmetical types are satisfied but which is not saturated enough. For this purpose, we build a hyperarithmetical recursively saturated elementary extension of each hyperarithmetical structure.
Keywords: arithmetical set, hyperarithmetical presentation, model saturated enough, $\omega$-saturated model, hereditarily finite superstructures, natural ordinals.
Received: 01.06.2010
English version:
Siberian Mathematical Journal, 2011, Volume 52, Issue 2, Pages 311–315
DOI: https://doi.org/10.1134/S0037446611020145
Bibliographic databases:
Document Type: Article
UDC: 510.5
Language: Russian
Citation: V. G. Puzarenko, “Existence of saturated structures”, Sibirsk. Mat. Zh., 52:2 (2011), 393–399; Siberian Math. J., 52:2 (2011), 311–315
Citation in format AMSBIB
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    		Сибирский математический журнал Siberian Mathematical Journal
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