Axiomatic Set TheoryThis clear and well-developed approach to axiomatic set theory is geared toward upper-level undergraduates and graduate students. It examines the basic paradoxes and history of set theory and advanced topics such as relations and functions, equipollence, finite sets and cardinal numbers, rational and real numbers, and other subjects. 1960 edition. |
Avis des internautes - Rédiger un commentaire
Aucun commentaire n'a été trouvé aux emplacements habituels.
Table des matières
| 1 | |
| 14 | |
| 57 | |
EQUIPOLLENCE FINITE SETS AND CARDINAL NUMBERS | 91 |
FINITE ORDINALS AND DENUMERABLE SETS | 127 |
RATIONAL NUMBERS AND REAL NUMBERS | 159 |
TRANSFINITE INDUCTION AND ORDINAL ARITHMETIC | 195 |
THE AXIOM OF CHOICE | 239 |
Autres éditions - Tout afficher
Expressions et termes fréquents
A X B arithmetic asserts axiom for cardinals axiom of choice axiom of extensionality axiom of regularity axiom schema cardinal numbers Cauchy sequence Chapter continuum Dedekind define definition DEFINrrIoN denumerable domain empty set equipollent equivalence relation exercise finite cardinals finite sets first element formulation fractions function f given infinite cardinal infinite set integer introduced intuitive JC(A limit ordinal logic mathematics maximal element mooF natural numbers non-negative rational numbers notation notion object language obvious ordered pairs ordinal addition ordinal arithmetic paradox partition PnooF power set primitive formula proof of Theorem Prove Theorem quantifier real numbers reflexive schema of replacement schema of separation sequence of real sequences of rational set theory special axiom Suppose Tarski Theorem 12 Theorem 28 THnoHEu THnonsu transfinite cardinal transfinite induction transfinite recursion unique upper bound variables virtue of Theorem well-ordered sets whence Zermelo Zermelo-Fraenkel set theory
Fréquemment cités
Page 5 - I should gladly have dispensed with this foundation if I had known of any substitute for it. And even now I do not see how arithmetic can be scientifically established; how numbers can be apprehended as logical objects, and brought under review; unless we are permitted — at least conditionally — to pass from a concept to its extension. May I always speak of the extension of a concept — speak of a class? And if not, how are the exceptional cases recognized? Can we always infer from one concept's...
Page 5 - Hardly anything more unfortunate can befall a scientific writer than to have one of the foundations of his edifice shaken after the work is finished. This was the position I was placed in by a letter of Mr Bertrand Russell, just when the printing of this volume was nearing its completion. It is a matter of my Axiom (V). I have never disguised from myself its lack of the self-evidence that belongs to the other axioms and that must properly be demanded of a logical law.
Page 24 - AUB is defined to be the set which consists of those objects x which belong to at least one of the sets A and B. The...
Page 138 - My own realm of thoughts, ie, the totality S of all things, which can be objects of my thought, is infinite. For if s signifies an element of S, then is the thought s', that s can be object of my thought, itself an element of JJ-.
Page 1 - By a set we mean any kind of a collection of entities of any sort.* Thus we can speak of the set of all Americans, or the set of all integers, or the set of all Americans and integers, or the set of all straight lines, or the set of all circles which pass through a given point. Many other words are used synonymously with 'set': for instance, 'class', 'collection', and 'aggregate'.
Page 187 - If a non-empty set of real numbers has an upper bound, then it has a least upper bound.
Page 5 - ... had known of any substitute for it. And even now I do not see how arithmetic can be scientifically established; how numbers can be apprehended as logical objects, and brought under review; unless we are permitted — at least conditionally — to pass from a concept to its extension. May I always speak of the extension of a concept — speak of a class? And if not, how are the exceptional cases recognized? Can we always infer from one concept's coinciding in extension with another concept that...
Page 5 - An occurrence of a variable in a formula is bound if and only if the occurrence is within the scope of a quantifier employing the variable, or is the occurrence in that quantifier.
Page 249 - A property of sets is said to be of finite character if a set has the property when and only when all its finite subsets have the property.
Références à ce livre
Informations bibliographiques
| Titre | Axiomatic Set Theory Dover Books on Mathematics Series Dover Books on advanced mathematics University series in undergraduate mathematics |
| Auteur | Patrick Suppes |
| Édition | intégrale, réimprimée, révisée |
| Éditeur | Courier Corporation, 1960 |
| ISBN | 0486616304, 9780486616308 |
| Longueur | 267 pages |
| Exporter la citation | BiBTeX EndNote RefMan |