At the «Taimanov Seminar on Model Theory», an invited professor delivered a talk on reverse mathematics and cryptology  

On January 27, 2026, a research talk was delivered within the framework of the Taimanov Seminar on Model Theory by Nikolai Alekseevich Bazhenov (Novosibirsk State University, Mathematical Center of Akademgorodok). The talk, entitled On Primitive Recursive Reverse Mathematics, attracted significant interest from researchers in cryptology and theoretical computer science.

In his presentation, the speaker discussed recent developments in reverse mathematics under primitive recursive restrictions. The focus was on identifying the minimal logical principles and computational resources required to prove specific mathematical statements. This approach provides a precise framework for comparing the proof-theoretic strength of theories while avoiding non-constructive methods.

Reverse mathematics is particularly relevant to cryptology, as it allows researchers to isolate the weakest assumptions underlying cryptographic algorithms and security proofs. Such an analysis is crucial for studying the correctness of reductions, formalizing computational hardness assumptions, and developing models with bounded resources that better reflect practical cryptographic settings. From the perspective of theoretical computer science, these methods are also highly relevant to formal verification and automated theorem proving.

The talk stimulated an active discussion and highlighted the growing role of reverse mathematics as a foundational tool for interdisciplinary research.