6 found
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  1.  28
    The Strength of Infinitary Ramseyan Principles Can Be Accessed by Their Densities.Andrey Bovykin & Andreas Weiermann - 2017 - Annals of Pure and Applied Logic 168 (9):1700-1709.
  2. Unprovability Threshold for the Planar Graph Minor Theorem.Andrey Bovykin - 2010 - Annals of Pure and Applied Logic 162 (3):175-181.
    This note is part of the implementation of a programme in foundations of mathematics to find exact threshold versions of all mathematical unprovability results known so far, a programme initiated by Weiermann. Here we find the exact versions of unprovability of the finite graph minor theorem with growth rate condition restricted to planar graphs, connected planar graphs and graphs embeddable into a given surface, assuming an unproved conjecture : ‘there is a number a>0 such that for all k≥3, and all (...))
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  3. Resplendent Models and $${\sigma_1^1}$$ -Definability with an Oracle.Andrey Bovykin - 2008 - Archive for Mathematical Logic 47 (6):607-623.
    In this article we find some sufficient and some necessary ${\Sigma^1_1}$ -conditions with oracles for a model to be resplendent or chronically resplendent. The main tool of our proofs is internal arguments, that is analogues of classical theorems and model-theoretic constructions conducted inside a model of first-order Peano Arithmetic: arithmetised back-and-forth constructions and versions of the arithmetised completeness theorem, namely constructions of recursively saturated and resplendent models from the point of view of a model of arithmetic. These internal arguments are (...)
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  4.  11
    Resplendent Models and $${\sigma_1^1}$$ -Definability with an Oracle.Andrey Bovykin - 2008 - Archive for Mathematical Logic 47 (6):607-623.
    In this article we find some sufficient and some necessary \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Sigma^1_1}$$\end{document} -conditions with oracles for a model to be resplendent or chronically resplendent. The main tool of our proofs is internal arguments, that is analogues of classical theorems and model-theoretic constructions conducted inside a model of first-order Peano Arithmetic: arithmetised back-and-forth constructions and versions of the arithmetised completeness theorem, namely constructions of recursively saturated and resplendent models from the point of view (...)
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  5.  6
    Exact Unprovability Results for Compound Well-Quasi-Ordered Combinatorial Classes.Andrey Bovykin - 2009 - Annals of Pure and Applied Logic 157 (2-3):77-84.
    In this paper we prove general exact unprovability results that show how a threshold between provability and unprovability of a finite well-quasi-orderedness assertion of a combinatorial class is transformed by the sequence-construction, multiset-construction, cycle-construction and labeled-tree-construction. Provability proofs use the asymptotic pigeonhole principle, unprovability proofs use Weiermann-style compression techniques and results from analytic combinatorics.
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  6.  1
    Resplendent Models and InlineEquation ID=" IEq1"> ImageObject FileRef=" 1532008100ArticleIEq1. Gif" Format=" GIF" Color=" BlackWhite" Type=" Linedraw" Rendition=" HTML"/> EquationSource Format=" TEX">. [REVIEW]Andrey Bovykin - 2008 - Archive for Mathematical Logic 47 (6):607-624.
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