2009 seminar talk: First-order theories without the independence property

Talk held by Hans Adler (KGRC) at the KGRC seminar on 2009-11-26.


Roughly speaking, a first-order formula has the independence property (relative to a complete theory T) if it cannot be used to represent arbitrary subsets of an infinite set in a model of T. T itself is said to have the independence property if one of its formulas has it. The independence property defines a very significant dividing line in the sense of Shelah. In the last years theories without the independence theory (also known as NIP theories) have received wider attention as a potentially fruitful generalisation of stable theories.

I will give an elementary introduction into this field, with a special focus on some of Shelah's remarkable results related to indiscernible sequences.

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Kurt Gödel Research Center for Mathematical Logic. Währinger Straße 25, 1090 Wien, Austria. Phone +43-1-4277-50501. Last updated: 2010-12-16, 04:37.