On the Model Theory of Random Graphs
On the Model Theory of Random Graphs
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Date
2009
Authors
Brody, Justin D.
Advisor
Laskowski, Michael C
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Abstract
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 "r."
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.