MATE-4140 Teoria de Modelos 1
Initiate studies of Model Theory of First-Order Logics. Completitude, Compacity, Lowenheim-Skolem Theorems, Categorical K-Theory, Complete Theories, Decidable and Undecidable Theory, Elementary Equivalence and Summersion. Characterization of Universal Theories, Universal-Existential. Existentially Closed Models, Complete Model Theories, Elimination of Quantifiers, Partial Isomorphisms, Feferman-Vaugth Theorems. Interpolation and Definibility Theorems. Automorphisms, Indiscernible, Ehrenfeucht-Mostowski Theorem. Fraissé Generic Models. Boolean Algebra, Filters, Ultra filters. Ultra products, Ultra product Saturation. Types of Elements, Types Realization and Omission, Saturation, Homogeneity, Universality. Atomic and Prime Models, Omega-Categoric Theories. Type Spaces, Stability, Stable Omega Theories. Keisler-Shelah Theorem, Characterization of Elementary Classes. Morley Categoricity Theorem. Baldwin-Lachlan Theorem. After all of the foregoing, the instructor may concentrate further on themes such as: Laws 0-1 in Finite Models. Finite Models Spectrum. Relations with Complexity.
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