Kolmogorov-Veloso Problems

 This paper (now in the arXiv)  Kolgomorov-Veloso Problems and Dialectica Categories was written last year for a book for Paulo Augusto Veloso, a friend, teacher and colleague at the Dept of Informatica, PUC-RJ in the 80s. The book appeared this year, A Question is More Illuminating than an Answer. A Festschrift for Paulo A. S. Veloso – February 15, 2021, edited by E. Hermann Haeusler, Luiz Carlos Pereira, and J. Petrucio Viana. 

 Samuel Gomes da Silva and I have been working for several years now on applications of the Dialectica construction to Set Theory (which is Samuel's speciality) and hearing Wagner Sanz talk about Veloso's Theory of Problems, we realized that Kolmogorov's problems were another case of the Dialectica construction. The examples from undergraduate/graduate mathematics that Samuel described to explain the connection are just beautiful!

Both Kolmogorov and Veloso had extremely general theories of problems that get much more concrete when we introduce the morphisms of category theory. I have given two talks about this work, one in the meeting called Finding the Right Abstractions and one more recently in the Logic Colloquium, organized in Poland.