Walks on Ordinals and Their Characteristics
Información General
- Autores: Stevo Todorcevic
- Editores: Basel : Birkhäuser, 2007
- Año de publicación: 2007
- País: Alemania
- Idioma: inglés
- ISBN: 978-3-7643-8528-6, 978-3-7643-8529-3
- Texto completo no disponible (Saber más ...)
Resumen
The walks on ordinals and analysis of their characteristics is a subject matter started by the author some twenty years ago in order to disprove a particular extension of the Ramsey theorem. A further analysis has shown however that the resulting method is quite useful in detecting critical mathematical objects in contexts where only rough classifications are possible. For example, many of the characteristics of walks on countable ordinals lead naturally to uncountable linear orderings whose Cartesian squares can be covered by countably many chains which turns out to be critical objects in the category of all linear orderings. Recently the method has led us to solutions to some other problems in a variety of disciplines such as for example a natural extension of the unconditional basic sequence problem from the Banach space theory or the famous L-space problem from topology.
The book gives a careful and comprehensive account of the method and gathers many of these applications in a unified and comprehensive manner.
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