Logic Seminar
Kota Takeuchi
University of Tsukuba
When do we have an indiscernible tree?
Abstract: In model theory indiscernible sequences are very important objects. The unstability of a theory is witnessed by a sequence with an order. Moreover, we can retake the witness by an indiscernible sequence. This technique is useful for classifying unstable theories. For example, Tree Property is defined by the existence of a tree with a structure on the tree. To prove n-TP iff 2-TP, we use the existence of an indiscernible tree witnessing n-TP. In this talk we discuss when we have an indiscernible tree which satisfies a condition (like n-TP). The answer depends on the structure of the tree, but we will see that in many cases if the condition has a suitable subtree property then it is realized by an indiscernible tree.
Wednesday June 13, 2012 at 3:00 PM in SEO 427