4 citations · 4 across the 7 of their papers we have counts for
13 papers · 1 filter
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…
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…
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…
On the unification problem for GLP
Lev D. Beklemishev
We show that the polymodal provability logic GLP, in a language with at least two modalities and one variable, has nullary unification type. More specifically, we show that the for…
Conservativity spectra and generalized Ignatiev model
Lev D. Beklemishev
We study a generalization of the notion of conservativity spectrum of an arithmetical theory to a language with transfinitely many truth definitions. We establish a correspondence…
Axiomatizing Origami planes
Lev Beklemishev, Anna Dmitrieva, Johann A. Makowsky
We provide a variant of an axiomatization of elementary geometry based on logical axioms in the spirit of Huzita--Justin axioms for the Origami constructions. We isolate the fragme…