Abstract
The material of this section is standard (with the exception of Theorem 11.19). We develop the rudiments of model-theoretic notions needed for the purpose of studying the fundamental properties of an ultraproduct; these properties are developed in this section, in § 12 and in § 13 below. The ultraproduct construction is given and the Theorem of Łoś (11.5), together with its Corollaries 11.6 and 11.7 (Compactness theorem), is proved. It is verified that an elementary type is an elementary Jónsson class (Theorem 11.11) whose elementarily α-homogeneous-universal and (more generally) special structures are characterized in terms of saturation (Theorem 11.18).
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© 1974 Springer-Verlag Berlin · Heidelberg
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Comfort, W.W., Negrepontis, S. (1974). Elementary Types. In: The Theory of Ultrafilters. Die Grundlehren der mathematischen Wissenschaften, vol 211. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-65780-1_11
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DOI: https://doi.org/10.1007/978-3-642-65780-1_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-65782-5
Online ISBN: 978-3-642-65780-1
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