we held a semianr in Logic and Set Theory
tomorrow, Tuesday, March 27.
Time 16:00-17:30, place: semianr room 201
Speaker: Artem Chernikov (Jerusalem)
Title: On the number of Dedekind cuts and NIP
For a cardinal k, we let ded(k) be the supremum of the number of Dedekind cuts a linear order of size k may have. While it is always true that k < ded(k) and that ded(k) is bounded by the exponent, everything else seems to depend on the model of ZFC one is working with. We establish some new equalities and inequalities, in particular answering a question of Keisler.
Model-theoretic importance of ded(k) comes from the fact that it describes the size of type-spaces of dependent theories (an important class of first-order theories containing both stable and o-minimal theories, but also e.g. algebraically closed valued fields and p-adics). We give some applications to the two-cardinal model transfer, stability functions and non-forking spectra of dependent theories.
Joint work with Itay Kaplan and Saharon Shelah.