Set theory and its logic
Belknap Press of Harvard University Press, 1969 - Logic, Symbolic and mathematical - 361 pages
This is an extensively revised edition of Mr. Quine's introduction to abstract set theory and to various axiomatic systematizations of the subject. The treatment of ordinal numbers has been strengthened and much simplified, especially in the theory of transfinite recursions, by adding an axiom and reworking the proofs. Infinite cardinals are treated anew in clearer and fuller terms than before. Improvements have been made all through the book; in various instances a proof has been shortened, a theorem strengthened, a space-saving lemma inserted, an obscurity clarified, an error corrected, a historical omission supplied, or a new event noted.
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ancestral argument arithmetic attributes Aussonderung axiom of choice axiom of infinity axiom schema Bernays Cantor's theorem class abstracts comprehension axioms comprehension premisses comprehension schema defined definition extensionality follows formula free variables Frege Func further Godel hence impredicative individuals infinite cardinals infinite classes ix)Fx least bound mathematical induction natural numbers Neumann Neumann-Bernays system notation notion number theory ordered pairs Ordg ordinal number ordinal sum primitive predicate Proof propositional functions prove ratios real numbers Russell's paradox schema of replacement sense sequence set theory sethood simply subclass theorem schemata theory of classes theory of types things tion transfinite recursion typical ambiguity ultimate classes virtual theory well-ordering Whitehead and Russell x c z x e a x e z x)(x e y y e z Zermelo's system