Qualifying Exam Syllabus
نویسندگان
چکیده
Basic constructions: The completeness and compactness theorems. The Löwenheim-Skolem theorem. Omitting types. Ultraproducts. Indiscernible sequences. Nice properties: Saturation, homogeneity, and the monster model. Elimination of imaginaries and Meq. Quantifier elimination. Model completeness. Countably categorical theories. Stable theories: Characterizations of a stable formula. Stable, superstable, and ω-stable theories. Forking via definability of types. Forking via dividing (in general theories). Properties of the nonforking independence relation. Canonical bases. Ranks: φ-2-rank, Morley rank, R∞-rank, U-rank. Pregeometries: Dimension. Trivial, modular, and locally modular pregeometries. The geometry associated to a pregeometry. The pregeometry on a minimal set. Plane curves and linearity.
منابع مشابه
Qualifying Exam Syllabus Proposal
Exam Committee Exam Logistics Committee Chairperson: Date: Prof. Monica Vazirani Thursday September 3, 2015 Committee Members: Time: Prof. Dan Romik 11AM-2PM Assoc. Fu Liu Location: Prof. Greg Kuperberg MSB 3106 Prof. Francisco J. Samaniego 1 Proposed Research Talk 1.1 The Catalan numbers and q-analogues. A lattice path is a sequence of North N(0, 1) and East E(1, 0) steps in the first quadrant...
متن کاملAlgebra Oral Qualifying Exam Syllabus
algebra is the study of fundamental algebraic structures that occur throughout mathematics: groups, rings, modules, categories, and fields—as well as maps between them. A solid grasp of algebra can be useful to students of all mathematical stripes, and accordingly the suggested syllabus is a “strong core plus more” model: a student preparing for an oral qualifying exam in algebra should (1) fee...
متن کاملUpdate of the European Association of Cardiovascular Imaging (EACVI) Core Syllabus for the European Cardiovascular Magnetic Resonance Certification Exam.
An updated version of the European Association of Cardiovascular Imaging (EACVI) Core Syllabus for the European Cardiovascular Magnetic Resonance (CMR) Certification Exam is now available online. The syllabus lists key elements of knowledge in CMR. It represents a framework for the development of training curricula and provides expected knowledge-based learning outcomes to the CMR trainees, in ...
متن کاملQualifying Exam
In order to satisfy qualifying exam requirements adhered to by the School of Informatics and Computing, I will provide an overview of global optimization techniques, specifically simulated annealing, genetic algorithms, and tabu seach.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011