A dependent theory with few indiscernibles

Itay Kaplan; Saharon Shelah

doi:10.1007/s11856-014-1067-2

A dependent theory with few indiscernibles

Itay Kaplan^*, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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,1iff κ → (δ)_θ ^<ω. This means that unless there are good set theoretical reasons, there are large sets with no indiscernible sequences.

Original language	American English
Pages (from-to)	59-103
Number of pages	45
Journal	Israel Journal of Mathematics
Volume	202
Issue number	1
DOIs	https://doi.org/10.1007/s11856-014-1067-2
State	Published - 2 Oct 2014

Bibliographical note

Funding 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. Received September 7, 2012 and in revised form May 31, 2013

Publisher Copyright:
© 2014, Hebrew University of Jerusalem.

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10.1007/s11856-014-1067-2

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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,1iff κ → (δ)θ <ω. This means that unless there are good set theoretical reasons, there are large sets with no indiscernible sequences.",

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N2 - 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,1iff κ → (δ)θ <ω. This means that unless there are good set theoretical reasons, there are large sets with no indiscernible sequences.

AB - 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,1iff κ → (δ)θ <ω. This means that unless there are good set theoretical reasons, there are large sets with no indiscernible sequences.

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A dependent theory with few indiscernibles

Abstract

Bibliographical note

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