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 |
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Pages (from-to) | 59-103 |
Number of pages | 45 |
Journal | Israel Journal of Mathematics |
Volume | 202 |
Issue number | 1 |
DOIs | |
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.