# Mathematical logic

Modern mathematical logic originated in the early 20th century from the foundational work of Gödel, Tarski, Turing, and many others. Over the last 50 years, the subject has developed over the last 50 years into an amalgam of fast-moving disciplines, each with its own sophisticated techniques.

These are linked by profound common concerns, around, for example:

- definability: what can be expressed by sentences in a formal languages;
- decidability: when there exists an algorithm to find out if a sentence follows from certain axioms;
- computability and computational complexity: what can be obtained algorithmically, and how efficiently;
- the nature of the continuum, or more generally, the behaviour of infinite sets;
- constructivism;
- the foundations of mathematics.

Some branches are highly multidisciplinary and force the researcher to be fully conversant with other fields (e.g. algebra, geometry, combinatorics, computer science, philosophy).

The Leeds Logic Group is one of the largest and most active logic groups worldwide. We have an international reputation for research in many of the main areas of mathematical logic, including computability theory, model theory, set theory, proof theory and categorical logic, as well as in applications to algebra, analysis, geometry, number theory, and theoretical computer science. We also have members in the Schools of Computing and of Philosophy.

We have been very successful in obtaining support from EPSRC, the EU, and several other sources for research students and postdoctoral fellows, and it has been the focus of extensive international collaborations via a number of major funded research networks in proof theory, computability theory, model theory, set theory and category theory. We have a large group of postgraduate research students and postdoctoral fellows, and we host regular seminars and events every year. Leeds has hosted the Logic Colloquium on many occasions.

As one of the strongest mathematical logic groups in the world, we contribute to the UK's excellent international standing in higher education and research. Our research builds an understanding of mathematics at a fundamental level, which can flow on to other areas of mathematics which have more direct applications.

### Further information

Visit our mathematical logic research group website.

### Research seminars

All upcoming seminars can be found in our events section.

### PhD projects

We have opportunities for prospective PhD students. Potential projects can be found in our postgraduate research opportunities directory.