HomeGroupsTalkMoreZeitgeist
This site uses cookies to deliver our services, improve performance, for analytics, and (if not signed in) for advertising. By using LibraryThing you acknowledge that you have read and understand our Terms of Service and Privacy Policy. Your use of the site and services is subject to these policies and terms.
Hide this

Results from Google Books

Click on a thumbnail to go to Google Books.

Loading...

The Theory of UltraFilters (Grundlehren Der Mathematischen Wissenschaften…

by W. W. Comfort

MembersReviewsPopularityAverage ratingConversations
6None2,101,913NoneNone
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.… (more)
Recently added bymorphismus, hmcmath, appleby
Henriksen (1) logic (1) math (1) RF (1)

None.

None
Loading...

Sign up for LibraryThing to find out whether you'll like this book.

No current Talk conversations about this book.

No reviews
no reviews | add a review
You must log in to edit Common Knowledge data.
For more help see the Common Knowledge help page.
Canonical title
Original title
Alternative titles
Original publication date
People/Characters
Important places
Important events
Related movies
Awards and honors
Epigraph
Dedication
First words
Quotations
Last words
Disambiguation notice
Publisher's editors
Blurbers
Original language
Canonical DDC/MDS

References to this work on external resources.

Wikipedia in English

None

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.

No library descriptions found.

Book description
Haiku summary

Quick Links

Popular covers

None

Rating

Average: No ratings.

Is this you?

Become a LibraryThing Author.

 

About | Contact | Privacy/Terms | Help/FAQs | Blog | Store | APIs | TinyCat | Legacy Libraries | Early Reviewers | Common Knowledge | 155,672,160 books! | Top bar: Always visible