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- W4299704726 abstract "We study model theoretic tree properties ($text{TP}, text{TP}_1, text{TP}_2$) and their associated cardinal invariants ($kappa_{text{cdt}}, kappa_{text{sct}}, kappa_{text{inp}}$, respectively). In particular, we obtain a quantitative refinement of Shelah's theorem ($text{TP} Rightarrow text{TP}_1 lor text{TP}_2$) for countable theories, show that $text{TP}_1$ is always witnessed by a formula in a single variable (partially answering a question of Shelah) and that weak $k-text{TP}_1$ is equivalent to $text{TP}_1$ (answering a question of Kim and Kim). Besides, we give a characterization of $text{NSOP}_1$ via a version of independent amalgamation of types and apply this criterion to verify that some examples in the literature are indeed $text{NSOP}_1$." @default.
- W4299704726 created "2022-10-02" @default.
- W4299704726 creator A5063315940 @default.
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- W4299704726 date "2015-05-03" @default.
- W4299704726 modified "2023-09-27" @default.
- W4299704726 title "On model-theoretic tree properties" @default.
- W4299704726 doi "https://doi.org/10.48550/arxiv.1505.00454" @default.
- W4299704726 hasPublicationYear "2015" @default.
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