Albert-Ludwigs-Universität Freiburg Mathematisches Institut Abteilung für mathematische Logik und Grundlagen der Mathematik

Seminar Modelltheorie

Literatur

• Ad1. Hans Adler, Strong theories, burden and weight. Preprint March 2007.
• Ad2. Hans Adler, Kim's Lemma for NTP₂ theories: a simpler proof of a result by Chernikov and Kaplan. Preprint . February 2011 (revised March 2014).
• BY-Ch. Itaï Ben-Yaacov and Artem Chernikov, An independence theorem for NTP₂ theories. The Journal of Symbolic Logic 79 (2014), 135-153. arXiv:1207.0289 .
• Ch. Artem Chernikov, Theories without the tree property of the second kind. Annals of Pure and Applied Logic 165 (2014) 695-723.
• Ch-K. Artem Chernikov and Itay Kaplan, Forking and dividing in NTP₂ theories. The Journal of Symbolic Logic 77 (2012) 1-20.
• T-Z. Katrin Tent and Martin Ziegler, A Course in Model Theory. Lecture Notes in Logic 40, Cambridge U.P. 2012.

Liste der Vorträge

1. Indiscernible arrays and burden. Abschnitte 1 und 2 von Ch, bis Lemma 2.2. Auch Proposition 13 von Ad1. (30.04 Müller)
2. Submultiplicativity of burden. Ch, vom Lemma 2.3 bis Corollary 2.9. (07.05 Gahlen)
3. Simple, NIP and NTP₂ theories. Dp-rank. Abschnitt 3 von Ch. Abschnitt 3 von Ad1 bis Corollary 11. (14.05 Kölbing)
4. Strict invariance. Abschnitt 4 von Ch bis Fact 4.6. (21.05 Stuber)
5. Forking = dividing over models. Ad2 . (28.05 Schandelmeier)
6. Array dividing. Abschnitt 1 von BY-Ch. (04.06)
7. The chain condition. Abschnitt 2 von BY-Ch. (18.06)
8. Amalgamation theorem and G-compactness. Abschnitt 3 von BY-Ch. (25.06)

Komplementärliteratur

• Cas1. Enrique Casanovas, Around NTP₂ Lecture Notes of the Model Theory Seminar Barcelona, July 2013. Revised April 2014.
• Cas2. Enrique Casanovas, Simple Theories and Hyperimaginaries. Lecture Notes in Logic 39, Cambridge U.P. 2011.
• Ch1. Artem Chernikov, On theories without the tree property of the second kind Thèse de doctorat en mathématiques Université Claude Bernard - Lyon 1. 2011.
• Ch-Hi. Artem Chernikov and Martin Hils, Valued difference fields and NTP₂. arXiv:1208.1341v3 August 2013.
• Ch-Ka-Si. Artem Chernikov, Itay Kaplan and Pierre Simon, Groups and fields with NTP₂. arXiv:1212.6213 April 2013.
• Ka-Us1. Itay Kaplan and Alexander Usvyatsov, Strict independence in dependent theories. arXiv:1208.4062 August 2012.
• Ka-Us2. Itay Kaplan and Alexander Usvyatsov, Additivity of the dp-rank. Transactions of the American Mathematical Society, 365(2013), 5783-5804.
• Si. Pierre Simon, A guide to NIP theories. To appear in Lecture Notes in Logic. February 2014.