We develop the basic concepts of logic and model theory required for applications to field theory. These include the Skolem-Löwenheim theorem, Łoš theorem and an ℵ1-saturation property for ultraproducts. Finally, we apply regular ultraproducts of families of models to the theory of finite fields.
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© 2008 Springer-Verlag Berlin Heidelberg
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(2008). Ultraproducts. In: Field Arithmetic. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, vol 11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77270-5_7
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DOI: https://doi.org/10.1007/978-3-540-77270-5_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77269-9
Online ISBN: 978-3-540-77270-5
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