Model theory (Logic III)

Spring term 2008/09

Syllabus

• reminder: structures, satisfaction, completeness theorem, compactness
• basic tools: substructures, homomorphisms, elementary embedding, elementary equivalence, diagram, elementary chain, Tarski test, …
• Löwenheim–Skolem–Tarski theorems, Łoś–Vaught test
• types, omitting types theorem, Ryll-Nardzewski theorem
• saturated, universal, and homogeneous models, uniqueness theorem
• reduced product, ultraproduct, Łoś theorem, elementary classes
• joint consistency theorem, Craig interpolation, Beth definability theorem
• Ehrenfeucht–Fraïssé games

Recommended reading

• C. C. Chang, H. J. Keisler, Model theory, Elsevier, 1990
• W. Hodges, A shorter model theory, Cambridge University Press, 1997
• D. Marker, Model theory: an introduction, Springer, 2002