Switch to: Citations

References in:

Calibrating Provability Logic: From Modal Logic to Reflection Calculus

In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 89-94 (1998)

Add references

You must login to add references.
  1. Worms, gaps, and hydras.Lorenzo Carlucci - 2005 - Mathematical Logic Quarterly 51 (4):342-350.
    We define a direct translation from finite rooted trees to finite natural functions which shows that the Worm Principle introduced by Lev Beklemishev is equivalent to a very slight variant of the well-known Kirby-Paris' Hydra Game. We further show that the elements in a reduction sequence of the Worm Principle determine a bad sequence in the well-quasi-ordering of finite sequences of natural numbers with respect to Friedman's gapembeddability. A characterization of gap-embeddability in terms of provability logic due to Lev Beklemishev (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • Topological completeness of the provability logic GLP.Lev Beklemishev & David Gabelaia - 2013 - Annals of Pure and Applied Logic 164 (12):1201-1223.
    Provability logic GLP is well-known to be incomplete w.r.t. Kripke semantics. A natural topological semantics of GLP interprets modalities as derivative operators of a polytopological space. Such spaces are called GLP-spaces whenever they satisfy all the axioms of GLP. We develop some constructions to build nontrivial GLP-spaces and show that GLP is complete w.r.t. the class of all GLP-spaces.
    Download  
     
    Export citation  
     
    Bookmark   17 citations  
  • A comparison of well-known ordinal notation systems for ε0.Gyesik Lee - 2007 - Annals of Pure and Applied Logic 147 (1):48-70.
    We consider five ordinal notation systems of ε0 which are all well-known and of interest in proof-theoretic analysis of Peano arithmetic: Cantor’s system, systems based on binary trees and on countable tree-ordinals, and the systems due to Schütte and Simpson, and to Beklemishev. The main point of this paper is to demonstrate that the systems except the system based on binary trees are equivalent as structured systems, in spite of the fact that they have their origins in different views and (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation