Walks on Countable Ordinals

Part of the Progress in Mathematics book series (PM, volume 263)


The space ω1 of countable ordinals is by far the most interesting space considered in this book. There are many mathematical problems whose combinatorial essence can be reformulated as problems about ω1, which is in some sense the smallest uncountable structure. What we mean by ‘structure’ is ω1 together with a system Cα (α < ω1) of fundamental sequences, i.e., a system with the following two properties:
  1. (a)

    Cα+1 = {α},

  2. (b)

    Cα is an unbounded subset of α of order-type ω, whenever α is a countable limit ordinal > 0.



Fundamental Sequence Countable Ordinal Aronszajn Tree Countable Limit Souslin Tree 
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Copyright information

© Birkhäuser Verlag AG 2007

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