Date of Award

2018

Document Type

Thesis

Degree Name

Bachelors

Department

Natural Sciences

First Advisor

McDonald, Patrick

Area of Concentration

Mathematics

Abstract

This thesis is an expository work on major results in stability theory, a subfield of mathematical logic. We begin by proving Morley's Categoricity Theorem, which states that a complete countable theory has one model in some uncountable power if and only if it has one model in every uncountable power. A necessary condition for this uncountable categoricity to hold is stability in some infinite power l, which states that for every set of size less than l there are fewer than l types thereover. We then develop a rich toolbox including transcendence rank, indiscernible sequences, and forking with the goal of proving the Stability Spectrum Theorem, which states that for every complete theory T, |T| arbitrary, there exist cardinals k(T) and m0 such that T is stable in m if and only if m = m0 + m

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