CBT and BDT for Order-Types

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


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.


Ordinal Number Cardinal Number Addition Theorem Homological Algebra Dual Version 
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© 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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