Axiomatic Theory of Sets and ClassesThe main notions of set theory -- including cardinals, ordinals, and transfinite induction -- are fundamental to all mathematics. This advanced undergraduate- and graduate-level text offers a thorough exploration that extends from the history of set theory and its paradoxes to connections with symbolic and mathematical logic. Advanced topics include relations and functions, equipollence, and more. 1971 edition. |
Contents
THE FORMALIZATION OF SET THEORY | 1 |
PROPOSITIONAL CALCULUS | 14 |
QUANTIFICATION | 35 |
Copyright | |
20 other sections not shown
Common terms and phrases
Assume axiom of choice Axiom Scheme bijection binary operation called cardinal Chapter choice function codomain construct countable deducible defined DEFINITION Let denoted denumerable disjoint dmn f dmn ƒ domain equipollent equivalence relation example Exercise exists a unique false false family of sets finite sets formula functional relation given graph Hence implies inclusion induction infinite injective integers inverse Let f map f map h Map X,Y Metaproof METATHEOREM natural numbers nonempty set notation obtain order-isomorphism ordered pair ordinal number ordinal sum partially ordered preordered class PROOF RULE proper class properties PROPOSITION Let prove PV Q real numbers recursion satisfying says set theory statement subset Suppose surjective THEOREM Let totally ordered transfinite true true Uiel unique map upper bound well-ordered sets well-ordering theorem X X Y Xiel Zorn's lemma