CMSA New Technologies in Mathematics: Doing Mathematics with Simple Types: Infinitary Combinatorics in Isabelle/HOL
Lawrence Paulson - University of Cambridge Computer Laboratory
Are proof assistants relevant to mathematics? One approach to this question is to explore the breadth of mathematical topics that can be formalised. The partition calculus was introduced by Erdös and R. Rado in 1956 as the study of “analogues and extensions of Ramsey’s theorem”. Highly technical results were obtained by Erdös-Milner, Specker and Larson (among many others) for the particular case of ordinal partition relations, which is concerned with countable ordinals and order types. Much of this material was formalised last year (with the assistance of Džamonja and Koutsoukou-Argyraki). Some highlights of this work will be presented along with general observations about the formalisation of mathematics, including ZFC, in simple type theory.