# Research group Mathematical logic

Logic as an academic subject is the study of reasoning, and mathematical logic is the study of mathematical reasoning in its various precise forms. This research group is active in several areas of the field including, constructive mathematics, type theory and category-theoretic logic, as well as the philosophical aspects of logic and mathematics.

## Group description

Research in logic at the mathematics department was initiated in the late 1960s with Per Martin-Löf and his seminal work on proof theory and type theory, and its applications to the foundations of constructive mathematics. Martin-Löf type theory is a widely used foundational theory both in computer science for checking and organizing formal proofs, and in logic as a touchstone for constructiveness. Much of the present research efforts in the group may be regarded as a continuation of this internationally influential research program. New connections with topology and category theory, especially homotopy theory, has arisen with the univalent foundations program.

## Some specific research topics

- Systems for the foundations of constructive mathematics: Type theory, especially Martin-Löf type theory and univalent foundations, constructive set theory, computer supported formalization (Agda, Coq)
- Category theory and Model theory of constructive systems: categorical logic and model theory, homotopy-theoretic models of type theory, internal models of type theory.
- Constructive mathematics: point-free methods in topology and analysis. Logic and Linguistics: constructive and computational semantics.

## Seminars

The Stockholm Logic Seminar meets regularly on Wednesdays 11.00 – 11:45. Organizers: Peter LeFanu Lumsdaine, Anders Mörtberg, Per Martin-Löf (emeritus).

Seminars are announced in the calendar at Stockholm Mathematics Centre, SMC

Web pages including older seminars

## Group members

### Group managers

Peter LeFanu Lumsdaine

Universitetslektor

### Members

Axel Ljungström

PhD Student

Per Martin-Löf

Professor emeritus

Anders Mörtberg

Universitetslektor

Errol Yuksel

PhD Student

Max Zeuner

PhD Student