Advanced Logic

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

When this module is taught in the Autumn term (Semester 1), there will be alternative assessment for Study Abroad students at King's for Semester 1 only.

SEMESTER 1 ONLY Study Abroad students: Summative assessment: 1 x 3500-word essay (100%) due in Assessment Period 1 (January).

WHOLE YEAR Study Abroad students: Summative assessment: 1 x 2-hour exam (100%) in Assessment Period 2.

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. 

Module description disclaimer

King’s College London reviews the modules offered on a regular basis to provide up-to-date, innovative and relevant programmes of study. Therefore, modules offered may change. We suggest you keep an eye on the course finder on our website for updates.

Please note that modules with a practical component will be capped due to educational requirements, which may mean that we cannot guarantee a place to all students who elect to study this module.

Please note that the module descriptions above are related to the current academic year and are subject to change.