On the Model Theory of Random Graphs

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Date
2009Author
Brody, Justin D.
Advisor
Laskowski, Michael C
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Show full item recordAbstract
Hrushovski's amalgamation construction can be used to join a
collection of finite graphs to produce a ``generic'' of this
collection. The choice of the collection and the way they are joined
are determined by a real-valued parameter α. Classical results
have shown that for α irrational in (0,1), the model theory
of the resulting structure is very well-behaved.
This dissertation examines analogous constructions for rational <italic>r</italic>.
Depending on the way in which the parameter's control of the
construction is defined, the model theory of the resulting generic
will be either very well-behaved or very wild. We characterize when
each of these situations occurs.