DISJOINT AMALGAMATION IN LOCALLY FINITE AEC
DISJOINT AMALGAMATION IN LOCALLY FINITE AEC
复制标题
局部有限 AEC 中的不相交合并
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
M. Laskowski
中科院分区：
文献类型：
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作者：
J. Baldwin;Martin Koerwien;M. Laskowski
摘要引入了局部有限抽象初等类的概念，并发展了局部有限抽象初等类的不相交$左（{le λ，k}右）$ -合并)理论。由此我们发现了一个完整的${L_{{omega _1},omega}}$句子${phi _r}$族，它a)齐次表征${aleph _r}$（改进了Hjorth[11]和Laskowski-Shelah[13]的结果并回答了[21]的一个问题），而b) ${phi _r}$提供了${L_{{omega _1},omega}}$中一类完整句子的模型的第一个例子，其中合并所包含的基数谱不是无或全。
Abstract We introduce the concept of a locally finite abstract elementary class and develop the theory of disjoint $left( { le lambda ,k}
ight)$ -amalgamation) for such classes. From this we find a family of complete ${L_{{omega _1},omega }}$ sentences ${phi _r}$ that a) homogeneously characterizes ${aleph _r}$ (improving results of Hjorth [11] and Laskowski–Shelah [13] and answering a question of [21]), while b) the ${phi _r}$ provide the first examples of a class of models of a complete sentence in ${L_{{omega _1},omega }}$ where the spectrum of cardinals in which amalgamation holds is other that none or all.