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A dependent theory with few indiscernibles

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Abstract

We give a full solution to the question of existence of indiscernibles in dependent theories by proving the following theorem: For every θ there is a dependent theory T of size θ such that for all κ and δ, κ → (δ) T,1 iff κ → (δ) <ω θ . This means that unless there are good set theoretical reasons, there are large sets with no indiscernible sequences.

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Authors and Affiliations

  1. Institute of Mathematics, The Hebrew University of Jerusalem, Givat Ram, Jerusalem, 91904, Israel

    Itay Kaplan & Saharon Shelah

Authors
  1. Itay Kaplan
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  2. Saharon Shelah
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Corresponding author

Correspondence to Itay Kaplan.

Additional information

Part of the first author’s PhD thesis.

The first author was partially supported by SFB grant 878.

The second author would like to thank the Israel Science Foundation for partial support of this research (Grants no. 710/07 and 1053/11).

No. 975 on the second author’s list of publications.

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Kaplan, I., Shelah, S. A dependent theory with few indiscernibles. Isr. J. Math. 202, 59–103 (2014). https://doi.org/10.1007/s11856-014-1067-2

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  • DOI: https://doi.org/10.1007/s11856-014-1067-2

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