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.
Bibliographical noteFunding 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
© 2014, Hebrew University of Jerusalem.