Facebook Twitter Pinterest
  • Alle Preisangaben inkl. MwSt.
Nur noch 1 auf Lager (mehr ist unterwegs).
Verkauf und Versand durch Amazon. Geschenkverpackung verfügbar.
Vicious Circles: On the M... ist in Ihrem Einkaufwagen hinzugefügt worden
+ EUR 3,00 Versandkosten
Gebraucht: Gut | Details
Zustand: Gebraucht: Gut
Kommentar: Book Ships Air Mail Via Parcel Force From Los Angeles, USA. No Deliveries to Pack Stations. Please expect up to 21 days for delivery. Orders may be subject to duties/taxes which are determined by country upon arrival. Very Clean Copy. Over 300,000 Amazon Orders Shipped....Buy With Confidence!
Möchten Sie verkaufen?
Zur Rückseite klappen Zur Vorderseite klappen
Hörprobe Wird gespielt... Angehalten   Sie hören eine Hörprobe des Audible Hörbuch-Downloads.
Mehr erfahren
Dieses Bild anzeigen

Vicious Circles: On the Mathematics of Non-Wellfounded Phenomena (Center for the Study of Language and Information Publication Lecture Notes, Band 60) (Englisch) Taschenbuch – 13. Juli 1996

5.0 von 5 Sternen 1 Kundenrezension

Alle Formate und Ausgaben anzeigen Andere Formate und Ausgaben ausblenden
Preis
Neu ab Gebraucht ab
Taschenbuch
"Bitte wiederholen"
EUR 25,49
EUR 25,49 EUR 20,20
4 neu ab EUR 25,49 3 gebraucht ab EUR 20,20
click to open popover

Es wird kein Kindle Gerät benötigt. Laden Sie eine der kostenlosen Kindle Apps herunter und beginnen Sie, Kindle-Bücher auf Ihrem Smartphone, Tablet und Computer zu lesen.

  • Apple
  • Android
  • Windows Phone

Geben Sie Ihre Mobiltelefonnummer ein, um die kostenfreie App zu beziehen.

Jeder kann Kindle Bücher lesen — selbst ohne ein Kindle-Gerät — mit der KOSTENFREIEN Kindle App für Smartphones, Tablets und Computer.



Produktinformation

Produktbeschreibungen

Pressestimmen

' … a book to learn from.' L'Enseignement Mathématique

Über das Produkt

Many assume that circular phenomena and mathematical rigour are irreconcilable. Barwise and Moss have undertaken to prove this assumption false. Vicious Circles is intended for use by researchers who use hypersets, although the book is accessible to people with widely differing backgrounds and interests.

Alle Produktbeschreibungen

Kundenrezensionen

5.0 von 5 Sternen
5 Sterne
1
4 Sterne
0
3 Sterne
0
2 Sterne
0
1 Stern
0
Siehe die Kundenrezension
Sagen Sie Ihre Meinung zu diesem Artikel

Top-Kundenrezensionen

Format: Taschenbuch
This book discusses recent advances in the general field of set theory. The authors study a variant of ZF in which the axiom of foundation is replaced by a new axiom allowing non-well-founded sets. Just as the naturals can be extended to the integers, and the integers to the rationals, and the reals to the complex numbers, in each case by positing new numbers that are the solutions to a class of equations, so this book posits an extension to any model of set theory consisting of the solutions to a class of (systems of) equations having no solutions in ZF. The simplest example is the equation
x = {x},
whose solution,
x = {{{{...}}}} (infinitely deep)
is not permitted in ZF, but exists and is unique in the authors' theory.
The purpose of this extension to ZF is to create a set theory in which certain circular or infinite phenomena from computer science and other fields, e.g. cyclic data streams, can be much more directly modeled than is now possible in ZF. Currently in ZF in order to represent a cyclic data stream one has to develop the aparatus for natural numbers, and then represent the stream to be a function from the natural numbers into some suitable set representing the type of data. But in the author's set theory the stream could be represented as an unfounded set that is the solution to a simple equation, and many of its properties could then be more easily deduced without resort to arithmetic.
I found this book absolutely fascinating, and I highly recommend it to anyone who has had a course in set theory. The theory in the book is quite elegant and satisfying.
I was delighted to learn that there is still room for new variations of the axioms of set theory, a subject I thought (probably naively) had been fairly static for 60 years.
Kommentar 3 Personen fanden diese Informationen hilfreich. War diese Rezension für Sie hilfreich? Ja Nein Feedback senden...
Vielen Dank für Ihr Feedback.
Wir konnten Ihre Stimmabgabe leider nicht speichern. Bitte erneut versuchen
Missbrauch melden

Die hilfreichsten Kundenrezensionen auf Amazon.com (beta)

Amazon.com: 5.0 von 5 Sternen 2 Rezensionen
55 von 57 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen Fasciniating look at a new extension of set theory 18. November 1999
Von David Jefferson - Veröffentlicht auf Amazon.com
Format: Taschenbuch Verifizierter Kauf
This book discusses recent advances in the general field of set theory. The authors study a variant of ZF in which the axiom of foundation is replaced by a new axiom allowing non-well-founded sets. Just as the naturals can be extended to the integers, and the integers to the rationals, and the reals to the complex numbers, in each case by positing new numbers that are the solutions to a class of equations, so this book posits an extension to any model of set theory consisting of the solutions to a class of (systems of) equations having no solutions in ZF. The simplest example is the equation
x = {x},
whose solution,
x = {{{{...}}}} (infinitely deep)
is not permitted in ZF, but exists and is unique in the authors' theory.
The purpose of this extension to ZF is to create a set theory in which certain circular or infinite phenomena from computer science and other fields, e.g. cyclic data streams, can be much more directly modeled than is now possible in ZF. Currently in ZF in order to represent a cyclic data stream one has to develop the aparatus for natural numbers, and then represent the stream to be a function from the natural numbers into some suitable set representing the type of data. But in the author's set theory the stream could be represented as an unfounded set that is the solution to a simple equation, and many of its properties could then be more easily deduced without resort to arithmetic.
I found this book absolutely fascinating, and I highly recommend it to anyone who has had a course in set theory. The theory in the book is quite elegant and satisfying.
I was delighted to learn that there is still room for new variations of the axioms of set theory, a subject I thought (probably naively) had been fairly static for 60 years.
15 von 15 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen First systematic exposition of the Anti-Foundation Axiom 23. April 2006
Von Glyfadiotis - Veröffentlicht auf Amazon.com
Format: Taschenbuch
As the title suggests, this is the first systematic exposition of classic set theory without the axiom of foundation. What replaces it, the anti-foundation axiom, allows sets to be members of themselves and it is this type of circularity that, as the authors claim, lies at the heart of understanding knowledge in interacting systems (like computing machines or game-theoretic agents or Liar-type sentences that refer to themselves).

What makes the whole endeavour work is that this new axiom is still consistent with the rest of ZF theory (a fact that is proved in the book) and in this sense the new theory can be thought as an "extention" of the traditional hierarchical construction of sets.

The book is written in textbook style in that it presents the material methodically and it is reasonably self-contained (a basic understanding of set theory and adequate motivation are enough).

I would have given 4 stars for poor binding and some typos (nothing serious though), but the quality of presentation and the fact that it includes answers to all problems more than make up for it.
Waren diese Rezensionen hilfreich? Wir wollen von Ihnen hören.