Exploring Synthetic Mathematics with Andrej Bauer: Foundations & Intuitionistic Logic 🧮

Andrej Bauer is our delightful guest in this long episode! We talk about intuitionistic logic, and how adopting an open minded attitude towards foundations of logic can help you discover new mathematical worlds!



Andrej has an incredible aptitude for taking complex ideas in logic and making them simple and compelling.



Here are some links to know more:



https://www.andrej.com/



https://math.andrej.com/








This is Part I of our episode.








A few of the works referenced in our chat:



1. The Countable Reals



https://arxiv.org/abs/2404.01256
Andrej Bauer, James E. Hanson

2. On Fixed-Point Theorems in Synthetic Computability



https://math.andrej.com/asset/data/recursion-theorem.pdf
Andrej Bauer

3. An Invitation to Smooth Infinitesimal Analysis



https://publish.uwo.ca/\~jbell/invitation%20to%20SIA.pdf
John L. Bell

4. Constructive Analysis



https://link.springer.com/book/10.1007/978-3-642-61667-9

Errett Bishop, Douglas Bridges

5. An introduction to fibrations, topos theory, the effective topos and modest sets



https://www.lfcs.inf.ed.ac.uk/reports/92/ECS-LFCS-92-208/

Wesley Phoa

6. The Effective Topos



https://www.dpmms.cam.ac.uk/~jmeh1/Research/Pub81-90/hyland-effectivetopos.pdf
lJ.M.E. Hyland

7. Realizability: An Introduction to its Categorical Side



https://www.amazon.com/Realizability-152-Introduction-Categorical-Foundations/dp/0444515844

Jaap van Oosten

8. Using the internal language of toposes in algebraic geometry



https://arxiv.org/abs/2111.03685

Ingo Blechschmidt

9. On synthetic undecidability in Coq, with an application to the Entscheidungsproblem



https://www.ps.uni-saarland.de/Publications/documents/ForsterEtAl\_2018\_On-Synthetic-Undecidability.pdf

Yannick Forster,Dominik Kirst, Gert Smolka

10. Synthetic topology of data types and classical spaces



https://www.cs.bham.ac.uk/~mhe/papers/barbados.pdf
Martın Escardo

11. Foundations of Constructive Mathematics: Metamathematical Studies



https://a.co/d/bz4zWUE

Michael J. Beeson