Fischbachau, September 16-22, 2018
Tutorial on Constructive Algebra
This course gives an introduction to (some aspects of) constructive algebra. Special emphasis is put on the use of entailment relations.
I hope to complement Thierry Coquand's summer school lectures at the Hausdorff Research Institute for Mathematics in Bonn, May 3-9, 2018. Please have a look at the respective course website for the slides and a recommended reading list. Coquand's lectures have been recorded.
Here are some suggestions for further reading:
Edwards has shed light on Kronecker's place in history. See also here and here. (Alas, lodged behind a pay wall.)
Hilbert's programme in abstract algebra has been put under scrutiny by Crosilla and Schuster; see here.
Lorenzen's contributions are currently being revived by Coquand, Lombardi, and Neuwirth; see here and here.
Richman's non-trivial uses of trivial rings will be mentioned twice in the course.
Here's an interesting paper on the roots of point-free topology.
Last but not least, the book is freely available on the arXiv!