Indiscernible extraction and Morley sequences
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Publication:509610
DOI10.1215/00294527-3800865zbMATH Open1397.03051arXiv1403.5763OpenAlexW1565601160MaRDI QIDQ509610
Publication date: 17 February 2017
Published in: Notre Dame Journal of Formal Logic (Search for Journal in Brave)
Abstract: We present a new proof of the existence of Morley sequences in simple theories. We avoid using the ErdH{o}s-Rado theorem and instead use only Ramsey's theorem and compactness. The proof shows that the basic theory of forking in simple theories can be developed using only principles from "ordinary mathematics", answering a question of Grossberg, Iovino and Lessmann, as well as a question of Baldwin.
Full work available at URL: https://arxiv.org/abs/1403.5763
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Foundations of classical theories (including reverse mathematics) (03B30) Axiomatics of classical set theory and its fragments (03E30) Classification theory, stability, and related concepts in model theory (03C45) Partition relations (03E02)
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