\(I_0\) and combinatorics at
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- 作者：Xianghui Shi ; Nam Trang
- 关键词：Axiom \(I_0\) ; \(\lambda ^+\) ; Aronszajn tree ; Square ; Weak square ; Stationary reflection ; Good scales ; Diamond ; \(\lambda \) ; Continuum hypothsis ; Generic absoluteness ; \(\lambda \) ; Goodness
- 刊名：Archive for Mathematical Logic
- 出版年：2017
- 出版时间：February 2017
- 年：2017
- 卷：56
- 期：1-2
- 页码：131-154
- 全文大小：
- 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematical Logic and Foundations; Mathematics, general; Algebra;
- 出版者：Springer Berlin Heidelberg
- ISSN：1432-0665
- 卷排序：56
文摘
We investigate the compatibility of \(I_0\) with various combinatorial principles at \(\lambda ^+\), which include the existence of \(\lambda ^+\)-Aronszajn trees, square principles at \(\lambda \), the existence of good scales at \(\lambda \), stationary reflections for subsets of \(\lambda ^{+}\), diamond principles at \(\lambda \) and the singular cardinal hypothesis at \(\lambda \). We also discuss whether these principles can hold in \(L(V_{\lambda +1})\).