| The Theory of Ultrafilters Contributor(s): Comfort, W. W. (Author), Negrepontis, S. (Author), Comfort, William Wistar (Author) |
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ISBN: 0387066047 ISBN-13: 9780387066042 Publisher: Springer OUR PRICE: $95.00 Product Type: Hardcover - Other Formats Published: November 1974 |
| Additional Information |
| BISAC Categories: - Mathematics | Topology - General |
| Dewey: 514 |
| LCCN: 74003673 |
| Series: Grundlehren Der Mathematischen Wissenschaften (Springer Hardcover) |
| Physical Information: 492 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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., to the Stone-Cech com- pactification process (implying the Tychonoff theorem on the compact- ness of products). Since these are two ways of describing the same mathematical object, it is reasonable to expect that a study of ultrafilters from these points of view will yield results and methods which can be fruitfully crossbred. This unifying aspect is indeed what we have attempted to emphasize in the present work. |