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CBT and BDT for Order-Types

  • Arie HinkisEmail author
Chapter
Part of the Science Networks. Historical Studies book series (SNHS, volume 45)

Abstract

Not all results of cardinal arithmetic can be transported to order-type arithmetic, or even to ordinal arithmetic. For example, Sierpiński (1947b p 74) noted that the Mean-Value Theorem (see  Sect. 25.2) cannot be extended to ordinals instead of cardinals: If M is a set of type ω + 1 and P a subset of M containing only the last element of M, so obviously P is of type 1, there is no subset of M that has type ω and contains P. Another example is a set A of order-type ω + η + ω* and a set B of order-type η; each is ordinally similar to a subset of the other (the conditions of CBT) but the two are not ordinally similar.

Keywords

Ordinal Number Cardinal Number Addition Theorem Homological Algebra Dual Version 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.The Cohn Institute for the History and Philosophy of Science and IdeasTel Aviv UniversityTel AvivIsrael

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