Chains, Antichains and Fences

Bernd S. W. Schröder
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Bernd S. W. Schröder: Lousiana Tech University, Program of Mathematics and Statistics

Chapter 2 in Ordered Sets, 2003, pp 25-53 from Springer

Abstract: Abstract Chains and antichains are arguably the most common kinds of ordered sets in mathematics. The elementary number systems ℕ , ℤ, ℚ and ℝ (with the exception of course being ℂ) are chains. Chains are also at the heart of set theory. The Axiom of Choice is equivalent to Zorn’s Lemma (which we will adopt as an axiom) and the Well-Ordering Theorem. Both latter results are results about chains.

Keywords: Maximal Element; Choice Function; Ordinal Number; Large Element; Maximal Chain (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1007/978-1-4612-0053-6_2

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