SoSe 2010 » Model Theory
Prof. Dr. Otto
Synopsis
Model Theory
This is a (2+1) course may be taken as one half of
a
"Vertiefungsmodul Logik"
(especially but not exclusively in connection
with "Finite Model Theory" to be offered in the coming
winter term)
Prerequisites: Basics of Mathematical Logic, e.g.,
Introduction to Mathematical Logic (QM)
Synopsis:
Model theory is concerned with the semantics of logical formalisms
and investigates the expressive power of logics through the study
of definability. Key questions are: which structural properties
can be axiomatised?; what are the available models?; and how can those
be further classified?
It thus examsines the relationship between syntactic features
of formalisations and structural properties expressed.
Technically at the center are methods for the construction
and transformation of suitable structures (models) and the examination
of the algebraic and combinatorial properties of these models.
Classical model theory primarily deals with first-order logic
as the logical formalism and develops techniques for the generation
and analysis of models for first-order theories, for the comparison
between models in algebraic and logical terms, and for the
classification of models w.r.t. logical and combinatorial criteria.
This course sets out to treat the following core topics:
-
model constructions, including ultra-products and elementary chains
among others
-
classical preservation theorems (syntax vs. closure properties;
expressive completeness results)
-
model theoretic games, back&forth, partial isomomorphy;
Lindstrom's theorem
-
types and saturation properties;
further expressive completeness results, countable models
and categoricity, Fraise limits and 0-1 laws
Literature
Cori/Lascar: Mathematical Logic
Chang/Keisler: Model Theory
Hodges: Model Theory
Hodges: A Shorter Model Theory
Marker: Model Theory, an Introduction
Rothmaler: Modelltheorie
Poizat: A Course in Model Theory
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