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Cookie akzeptierenS. Negrepontis / W. W. Comfort
The Theory of Ultrafilters
- Springer Berlin Heidelberg
- 2011
- Taschenbuch
- 500 Seiten
- ISBN 9783642657825
An ultrafilter is a truth-value assignment to the family of subsets of a set, and a method of convergence to infinity. From the first (logical) property arises its connection with two-valued logic and model theory; from the second (convergence) property arises its connection with topology and set theory. Both these descriptions of an ultrafilter are connected with compactness. The model-theoretic property finds its expression in the construction of the ultraproduct and the compactness type of theorem of Los (implying the compactness theorem of first-order logic); and the convergence property leads to the process of completion by the adjunction of an ideal element for every ultrafilter-i. e.
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