Module description
Set Theory is important for the philosophy of mathematics and metaphysics. In this course we look at naive set theory and the paradoxes that were found in it by Russell and others; these paradoxes led to a reconstruction of the foundations of mathematics on axiomatic grounds. We will look at one such axiomatisation of set theory - Zermelo - Fraenkel set theory. Within this theory we can develop fundamental mathematical concepts that are widely used in philosophy and logic, such as the ideas of relations, partial orders, functions, partitions and equivalence classes. We also look at how natural numbers and other mathematically useful objects can be represented using sets, and we then develop a theory of the infinite using transfinite ordinal and cardinal numbers.
Assessment details
Summative assessment: 1 x 2 hour examination (100%)
Formative assessment: 4 sets of exercises
Educational aims & objectives
The module aims to provide the fundamental notions of proof-theory: the sequent calculus for predicate logic, the cut-elimination theorem, and the proof-theoretic analysis of mathematical theories.
Teaching pattern
One one-hour weekly lecture and one one-hour weekly seminar over ten weeks.