3 papers
math.LO2025
Fragments of arithmetic and cyclic proofs
Lev D. Beklemishev, Daniyar S. Shamkanov, Ivan N. Smirnov
We present an alternative cyclic proof system for Peano arithmetic that could be simpler than the existing ones and well-adapted both for proof analysis and for automatizing induct…
math.LO2024
Automatic structures and the problem of natural well-orderings
Lev D. Beklemishev, Fedor N. Pakhomov
We explore the idea of using automatic and similar kind of presentations of structures to deal with the conceptual problem of natural proof-theoretic ordinal notations. We conclude…
math.LO2024
Periodic frames
Lev D. Beklemishev, Yunsong Wang
Polymodal provability logic GLP is incomplete w.r.t. Kripke frames. It is known to be complete w.r.t. topological semantics, where the diamond modalities correspond to topological…