This Festschrift is published in honor of Yuri Gurevich's 80th birthday. An associated conference, YuriFest 2020, was planned for May 18-20 in Fontainebleau, France, in combination with the 39th Journees sur les Arithmetiques Faibles also celebrating Yuri's 80th birthday. Because of the coronavirus situation, the conference had to be postponed, but this Festschrift is being published as originally planned. It addresses a very wide variety of topics, but by no means all of the fields of logic and computation in which Yuri has made important progress.

The field of weak arithmetics is an application of logical methods to number theory that was developed by mathematicians, philosophers, and theoretical computer scientists. This third volume in the weak arithmetics collection contains nine substantive papers based on lectures delivered during the two last meetings of the conference series Journees sur les Arithmetiques, held in 2014 at the University of Gothenburg, Sweden, and in 2015 at the City University of New York Graduate Center.