## Abstract

The space

*ω*_{1}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*ω*_{1}, which is in some sense the smallest uncountable structure. What we mean by ‘structure’ is*ω*_{1}together with a system*C*_{α}(*α*<*ω*_{1}) of fundamental sequences, i.e., a system with the following two properties:- (a)
*C*_{α+1}= {*α*}, - (b)
*C*_{α}is an unbounded subset of*α*of order-type*ω*, whenever*α*is a countable limit ordinal > 0.

## Keywords

Fundamental Sequence Countable Ordinal Aronszajn Tree Countable Limit Souslin Tree
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

© Birkhäuser Verlag AG 2007