A new class of order types

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Let φ4 be the class of all order-types φ{symbol} with the properties that every uncountable subtype of φ{symbol} contains an uncountable well-ordering, but φ{symbol} is not the union of countably many well-orderings. It is proved that φ4 ≠ 0, and a way is found of associating stationary sets with most of the types in φ4 which is useful for applications. A number of results concerning the structure and embeddability properties of φ4 are obtained, including some consistency and independence results. One consequence is the independence of Jensen's combinatorial principle □ω1. © 1976.




Baumgartner, J. E. (1976). A new class of order types. Annals of Mathematical Logic, 9(3), 187–222. https://doi.org/10.1016/0003-4843(76)90001-2

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