Set Theory

Set theory is a mathematical theory of collections, taken as objects in their own right. According to folklore, set theory provides a foundation for all of mathematics. Its central concepts are also widely employed in other fields, such as in philosophy and linguistics. The main goals of the course are (i) to introduce you to the theory of sets in an axiomatic setting, and (ii) to equip you to engage in philosophical reflection on set theory and its applications. Some topics we will tackle include: how to “construct” various mathematical objects in set theory; cardinals and ordinals; controversial axioms (e.g., choice, replacement, and so-called “large cardinal” axioms); how we might justify our choices of axioms.