Set theory and logic

Robert R. Stoll.

Edité par

Hbk, xiv, 474 pages. Foxing to edges and end-papers o/w a clean copy in good condition. Dust-wrapper scuffed around edges but still in good condition. Contents Sets and relations : Cantor's concept of a set ; The basis of intuitive set theory ; Inclusion ; Operations for sets ; The algebra of sets ; Relations ; Equivalence relations ; Functions ; Composition and inversion for functions ; Operations for collections of sets ; Ordering relations -- The natural number sequence and its generalizations : The natural number sequence ; Proof and definition by induction ; Cardinal numbers ; Countable sets ; Cardinal arithmetic ; Order types ; Well-ordered sets and ordinal numbers ; The axiom of choice, the well-ordering theorem, and Zorn's lemma ; Further properties of cardinal numbers ; Some theorems equivalent to the axiom of choice ; The paradoxes of intuitive set theory -- The extension of the natural numbers to the real numbers : The system of natural numbers ; Differences ; Integers ; Rational numbers ; Cauchy sequences of rational numbers ; Real numbers ; Further properties of the real number system -- Logic : The statement calculus. sentential connectives ; The statement calculus. truth tables ; The statement calculus. validity ; The statement calculus. consequence ; The statement calculus. applications ; The predicate calculus. symbolizing everyday language ; The predicate calculus. a formulation ; The predicate calculus. validity ; The predicate calculus. consequence -- Informal axiomatic mathematics : The concept of an axiomatic theory ; Informal theories ; Definitions of axiomatic theories by set-theoretical predicates ; Further features of informal theories -- Boolean algebras : A definition of a Boolean algebra ; Some basic properties of a Boolean algebra ; Another formulation of the theory ; Congruence relations for a Boolean algebra ; Representations of Boolean algebras ; Statement calculi as Boolean algebras ; Free Boolean algebras ; Applications to the theory of Boolean algebras to statement calculi ; Further interconnections between Boolean algebras and statement calculi -- Informal axiomatic set theory : The axioms of extension and set formation ; The axiom of pairing ; The axioms of union and power set ; The axiom of infinity ; The axiom of choice ; The axiom schemas of replacement and restriction ; Ordinal numbers ; Ordinal arithmetic ; Cardinal numbers and their arithmetic ; The von Neumann-Bernays-Gödel theory of sets -- Several algebraic theories : Features of algebraic theories ; Definition of a semigroup ; Definition of a group ; Subgroups ; Coset decompositions and congruence relations for groups ; Rings, integral domains, and fields ; Subring and difference rings ; A characterization of the system of integers ; A characterization of the system of rational numbers ; A characterization of the real number system -- First-order theories : Formal axiomatic theories ; The statement calculus as a formal axiomatic theory ; Predicate calculi of first order as formal axiomatic theories ; First-order axiomatic theories ; Metamathematics ; Consistency and satisfiability of sets of formulas ; Consistency, completeness, and categoricity of first-order theories ; Turing machines and recursive functions ; Some undecidable and some decidable theories ; Gödel's theorems ; Some further remarks about set theory. [Logic, Symbolic and mathematical - Aggregates (Building materials)] w14 / m16519. N° de réf. du vendeur 016519

Détails bibliographiques

Titre : Set theory and logic
Reliure : Hardcover
Etat : Good
Etat de la jaquette : Good