Summary: Quantifier Elimination and Real Closed
Ordered Fields with a Predicate for the Powers
December 17, 2005
In this thesis we first review the model theory of quantifier elim-
ination and investigate the logical relations among various quantifier
elimination tests. In particular we prove the equivalence of two quanti-
fier elimination tests for countable theories. Next we give a procedure
for eliminating quantifiers for the theory of real closed ordered fields
with a predicate for the powers of two. This result was first obtained
by van den Dries . His method is model-theoretic, which provides
no apparent bounds on the complexity of a decision procedure. In the
last section we give a complete axiomatization of the theory of real
closed ordered fields with a predicate for the Fibonacci numbers.
I thank my advisor Jeremy Avigad for the guidance he has provided me.
I am grateful to James Cummings and Rami Grossberg for many helpful