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A formalization of set theory without variables (Record no. 5809)

000 -Label
leader 03555nac 22003251u 4500
010 ## - ISBN
ISBN 9780821810415
qualificatif rel.
090 ## - Numéro biblio (koha)
Numéro biblioitem (koha) 5809
001 - Numéro de notice
Numéro d'identification notice 5809
101 ## - Langue
langue du document anglais
102 ## - Pays de publication ou de production
pays de publication Etats Unis
100 ## - Données générales de traitement
données générales de traitement 20091130 frey50
200 ## - Titre
titre propre A formalization of set theory without variables
type de document Monographie
Auteur Alfred Tarski and Steven Givant
210 ## - Editeur
lieu de publication Providence
nom de l'éditeur American Mathematical Society
date de publication 1987
215 ## - Description
Importance matérielle 1 vol. (xxi, 318 p.)
format 26 cm
225 ## - collection
titre de la collection Colloquium publications
numérotation du volume 41
ISSN de la collection ou de la sous-collection 0065-9258
lien interne koha 169109
320 ## - Note
note Bibliography: p. 273-282. Index
330 ## - Résumé
Résumé Completed in 1983, this work culminates nearly half a century of the late Alfred Tarski's foundational studies in logic, mathematics, and the philosophy of science. Written in collaboration with Steven Givant, the book appeals to a very broad audience, and requires only a familiarity with first-order logic. It is of great interest to logicians and mathematicians interested in the foundations of mathematics, but also to philosophers interested in logic, semantics, algebraic logic, or the methodology of the deductive sciences, and to computer scientists interested in developing very simple computer languages rich enough for mathematical and scientific applications.

The authors show that set theory and number theory can be developed within the framework of a new, different, and simple equational formalism, closely related to the formalism of the theory of relation algebras. There are no variables, quantifiers, or sentential connectives. Predicates are constructed from two atomic binary predicates (which denote the relations of identity and set-theoretic membership) by repeated applications of four operators that are analogues of the well-known operations of relative product, conversion, Boolean addition, and complementation. All mathematical statements are expressed as equations between predicates. There are ten logical axiom schemata and just one rule of inference: the one of replacing equals by equals, familiar from high school algebra.

Though such a simple formalism may appear limited in its powers of expression and proof, this book proves quite the opposite. The authors show that it provides a framework for the formalization of practically all known systems of set theory, and hence for the development of all classical mathematics.

The book contains numerous applications of the main results to diverse areas of foundational research: propositional logic; semantics; first-order logics with finitely many variables; definability and axiomatizability questions in set theory, Peano arithmetic, and real number theory; representation and decision problems in the theory of relation algebras; and decision problems in equational logic. (source : AMS)
410 ## - collection
lien interne koha 169106
Editeur AMS
titre Colloquium publications
numéro de volume 0041
ISSN 0065-9258
676 ## - annee msc
annee msc 2010
686 ## - Classification MSC
Indice 03E20
lien interne koha 161225
Libellé Mathematical logic and foundations -- Set theory
Sous-catégorie Other classical set theory (including functions, relations, and set algebra)
code du système msc
686 ## - Classification MSC
Indice 03-02
lien interne koha 161133
Libellé Mathematical logic and foundations
Sous-catégorie Research exposition (monographs, survey articles)
code du système msc
700 ## - Auteur
auteur Tarski
partie du nom autre que l'élément d'entrée Alfred
code de fonction Auteur
koha internal code 171308
dates 1901-1983
701 ## - coauteur
koha internal code 171583
nom Givant
prénom Steven R.
dates 1943-
code de fonction Auteur
856 ## - accès
URI http://zbmath.org/?q=an:0654.03036
note Zentralblatt
856 ## - accès
URI http://www.ams.org/mathscinet-getitem?mr=920815
note MathSciNet
856 ## - accès
URI http://www.ams.org/bookstore-getitem/item=COLL-41
note AMS
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