Ordered Sets, Induction, and the Axiom of Choice

  • George M. Bergman
Part of the Universitext book series (UTX)


Partially ordered sets are studied, and the techniques of inductive proofs and recursive constructions over partially ordered sets with ascending or descending chain condition is formalized. The axioms of Zermelo–Fraenkel Set Theory with Choice, and the arithmetic of ordinals and cardinals, are reviewed, and Zorn’s Lemma is developed. We end with some thoughts on whether set theory is “real”.


Natural Number Chain Condition Fibonacci Number Inductive Proof Recursive Construction 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • George M. Bergman
    • 1
  1. 1.Department of MathematicsUniversity of California, BerkeleyBerkeleyUSA

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