21 - 22 May 2022, Meeting in Internal Categoricity, Helsinki (Finland) & Virtual

The categoricity of an axiom system means that its non-logical symbols have, up to isomorphism, only one possible interpretation. The first axiomatizations of mathematical theories such as number theory and analysis by Dedekind, Hilbert, Huntington, Peano and Veblen were indeed categorical. These were all second order axiomatisations, suffering from what many consider a weakness, namely dependence on a strong metatheory, casting a shadow over these celebrated categoricity results. In finer analysis a new form of categoricity has emerged. It is called internal categoricity because it is perfectly meaningful without any reference to a metatheory, and it is now known that the classical theories, surprisingly even in their first order formulation, can be shown to be internally categorical.

In this workshop various aspects of and approaches to internal categoricity are presented and the following questions, among others, are discussed: What is the philosophical import/advantage of internal categoricity over ordinary categoricity? Is internal categoricity the right concept of categoricity? Does internal categoricity play a role also in first order theories?