Todorčević's work involves mathematical logic, set theory, and their applications to pure mathematics.
In Todorčević's 1978 master’s thesis, he constructed a model of MA + ¬wKH in a way to allow him to make the continuum any regular cardinal, and so derived a variety of topological consequences. Here MA is an abbreviation for Martin's axiom and wKH stands for the weak Kurepa Hypothesis.[6]
In 1980, Todorčević and Abraham proved the existence of rigid Aronszajn trees and the consistency of MA + the negation of the continuum hypothesis + there exists a first countable S-space.[7]
Awards and honours
Todorčević is the winner of
the first prize of the Balkan Mathematical Society for 1980 and 1982,[8]
the Shoenfield prize of the Association for Symbolic Logic for "outstanding expository writing in the field of logic" in 2013, for his book Introduction to Ramsey Spaces.[10][IRS]
He was selected by the Association for Symbolic Logic as their 2016 Gödel Lecturer.[11]