A new class of order types
A new class of order types
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一类新的订单类型
DOI：
10.1016/0003-4843(76)90001-2
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发表时间：
1976
期刊：
影响因子：
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通讯作者：
J. Baumgartner
中科院分区：
文献类型：
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作者：
J. Baumgartner
设φ 4是所有序类型的类，其性质是每个不可数的子类型都包含不可数的良序，但不可数的良序不是可数多良序的并集。证明了φ 4 ≠ 0，并找到了一种将平稳集与φ 4中的大多数类型联系起来的方法，这对实际应用是有用的。得到了关于φ 4的结构和可嵌入性的一些结果，包括一些相容性和独立性结果.一个推论是詹森组合原理□ ω 1的独立性。
Letφ4be the class of all order-types ϕ with the properties that every uncountable subtype of ϕ contains an uncountable well-ordering, but ϕ is not the union of countably many well-orderings. It is proved thatφ4≠ 0, and a way is found of associating stationary sets with most of the types inφ4which is useful for applications. A number of results concerning the structure and embeddability properties ofφ4are obtained, including some consistency and independence results. One consequence is the independence of Jensen's combinatorial principle □ω1.