An Even Shorter Model Theory
نویسنده
چکیده
These notes were prepared for the UC Berkeley Group in Logic & the Methodology of Science foundations exam. Material is adapted from Chang and Keisler’s (1973) Model Theory and Wilfrid Hodges’ (1997) A Shorter Model Theory. Sections 1-2 review basic semantic/syntactic concepts; Section 3 introduces Robinson diagrams and canonical interpretations; Section 4 presents backand-forth techniques; Section 5 introduces the method of quantifier elimination; Section 6 discusses Compactness and types; Section 7 examines atomic and saturated models; Section 8 presents the theorems of Löwenheim-Skolem; Section 9 examines preservation phenomena; Section 10 presents amalgamations and Fräısse limits; Section 11 discusses interpolation; Section 12 discusses modelcompleteness; Section 13 covers further miscellaneous topics.
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