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\(I_0\) and combinatorics at \(\lambda ^+\)

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Abstract

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 \(L(V_{\lambda +1})\).

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Authors and Affiliations

  1. School of Mathematical Sciences, Beijing Normal University, Key Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing, 100875, People’s Republic of China

    Xianghui Shi

  2. Department of Mathematics, University of California, Irvine, Irvine, CA, 92697-3875, USA

    Nam Trang

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  1. Xianghui Shi
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  2. Nam Trang
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Correspondence to Xianghui Shi.

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Shi, X., Trang, N. \(I_0\) and combinatorics at \(\lambda ^+\) . Arch. Math. Logic 56, 131–154 (2017). https://doi.org/10.1007/s00153-016-0518-3

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