Abstract
The theory of Jónsson classes is the setting of proper generality for the application of the classical principle of back-and-forth induction of Cantor and Hausdorff. Cantor conceived of this principle and used it to prove that the set of rational numbers is described as an ordered set by the following properties: it is countable, without a least or a greatest element, and densely ordered. Hausdorff generalized this result in his theory of η α -sets (studied in § 5 below). Erdős-Gillman-Henriksen proved similar results for the theory of real-closed fields.
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© 1974 Springer-Verlag Berlin · Heidelberg
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Comfort, W.W., Negrepontis, S. (1974). The General Theory of Jónsson Classes. 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_4
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DOI: https://doi.org/10.1007/978-3-642-65780-1_4
Publisher Name: Springer, Berlin, Heidelberg
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