The Axiom of ChoiceCourier Corporation, 09.04.2013 - 224 Seiten Comprehensive in its selection of topics and results, this self-contained text examines the relative strengths and consequences of the axiom of choice. Each chapter contains several problems, graded according to difficulty, and concludes with some historical remarks. An introduction to the use of the axiom of choice is followed by explorations of consistency, permutation models, and independence. Subsequent chapters examine embedding theorems, models with finite supports, weaker versions of the axiom, and nontransferable statements. The final sections consider mathematics without choice, cardinal numbers in set theory without choice, and properties that contradict the axiom of choice, including the axiom of determinacy and related topics |
Häufige Begriffe und Wortgruppen
aleph applications assume assumption atoms automorphisms Axiom of Choice basic Boolean algebra cardinal Chapter choice function choose compact complete condition Consequently consider consistent construct contains contradiction countable define determined disjoint elements Embedding Theorem equivalent Example exists extension fact fails filter find finite sets finite subsets fix formula function f given gives Hence holds homogeneous implies independence infinite isomorphic least support Lemma linear linearly ordered Math maximal measure method model of ZF Mostowski normal Note Notice numbers operations Ordering Principle ordinals pairs partition permutation model present Prime Ideal Theorem Principle Problem proof properties prove quantum mechanics real numbers regular relation result satisfies satisfy sequence set of reals set theory space statement symmetric symmetric model transitive ultrafilter union universal values well-ordered