By W. Wistar Comfort, Stylianos Negrepontis (auth.)
An ultrafilter is a truth-value task to the kin of subsets of a collection, and a mode of convergence to infinity. From the 1st (logical) estate arises its reference to two-valued common sense and version thought; from the second one (convergence) estate arises its reference to topology and set conception. either those descriptions of an ultrafilter are hooked up with compactness. The model-theoretic estate reveals its expression within the building of the ultraproduct and the compactness kind of theorem of Los (implying the compactness theorem of first-order logic); and the convergence estate ends up in the method finishing touch through the adjunction of an excellent point for each ultrafilter-i. e. , to the Stone-Cech com pactification strategy (implying the Tychonoff theorem at the compact ness of products). considering that those are methods of describing an analogous mathematical item, it's moderate to anticipate learn of ultrafilters from those issues of view will yield effects and strategies that are fruitfully crossbred. This unifying element is certainly what we now have tried to stress within the current work.
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