Topics in Logic: Consistency Strength

Course Description: What are the basic principles of mathematical reasoning? Logicians have developed a vast array of axiom systems that map out the possible answers to this question. This leaves the task of selecting among competing axiom systems. The main metric for comparing axiom systems is known as consistency strength. We will start by reviewing classic results on consistency strength. We will then turn to contemporary research that addresses one of the central mysteries in the foundations of mathematics, namely, that all natural axiom systems are comparable according to consistency strength.

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