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The generic pair conjecture for dependent finite diagrams

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Abstract

This paper generalizes Shelah’s generic pair conjecture (now theorem) for the measurable cardinal case from first order theories to finite diagrams. We use homogeneous models in the place of saturated models.

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Author information

Authors and Affiliations

  1. Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, Jerusalem, 91904, Israel

    Itay Kaplan, Noa Lavi & Saharon Shelah

  2. Department of Mathematics, Rutgers, The State University of New Jersey Hill Center-Busch Campus, 110 Frelinghuysen Road, Piscataway, NJ, 08854-8019, USA

    Saharon Shelah

Authors
  1. Itay Kaplan
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  2. Noa Lavi
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  3. Saharon Shelah
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Corresponding author

Correspondence to Itay Kaplan.

Additional information

The research leading to these results has received funding from the European Research Council, ERC Grant Agreement n. 338821.

The first author would like to thank the Israel Science Foundation for partial support of this research (Grant no. 1533/14).

No. 1055 on the third author’s list of publications.

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Kaplan, I., Lavi, N. & Shelah, S. The generic pair conjecture for dependent finite diagrams. Isr. J. Math. 212, 259–287 (2016). https://doi.org/10.1007/s11856-016-1286-9

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  • DOI: https://doi.org/10.1007/s11856-016-1286-9

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