Media Summary: Talk given Monday, July 13, 2015 at CMO-BIRS Oaxaca Abstract: A remarkable theorem of Shelah says that an unsimple We complete the proof of Scow's theorem that generalized indiscernibles correspond to Ramsey classes of finite structures. We prove the local character of dividing in simple theories, and introduce rank.
Model Theoretic Tree Properties - Detailed Analysis & Overview
Talk given Monday, July 13, 2015 at CMO-BIRS Oaxaca Abstract: A remarkable theorem of Shelah says that an unsimple We complete the proof of Scow's theorem that generalized indiscernibles correspond to Ramsey classes of finite structures. We prove the local character of dividing in simple theories, and introduce rank. We use rank to upgrade the local character of dividing to the local character of forking in simple theories. We describe extraction of ... We define Morley sequences and relate them to Morley sequences in invariant types (which had been discussed previously). We begin developing NTP_2 theories. We prove that TP_2 is always witnessed by a formula in a single free variable.
In this session, we introduce generalize indiscernibles and Ramsey classes of finite structures. We prove Kim's Lemma for Kim-dividing in NSOP_1 theories and show it characterizes NSOP_1 theories. We conclude the proof that NTP_2 is always witnessed by a formula in a single free variable and discuss some consequences.
