Paper: The Finite Length Property of the Rado Graph and Friends (at LICS 2026)

Authors: Jingjie Yang Mikołaj Bojańczyk Bartek Klin

Open access: https://doi.org/10.4230/LIPIcs.LICS.2026.82

Abstract

An infinite structure has the finite length property (over a given field) if, for each of its finite powers, chains of equivariant subspaces in the corresponding free vector space are bounded in length. Prior work showed that the countable pure set and the countable dense linear order without endpoints have this property. We generalise these results to (a) any structure approximated by finite substructures with few orbits, provided the field is of characteristic zero, and (b) any Fraïssé limit with free amalgamation in a finite vocabulary consisting of unary and binary relations, possibly expanded with a generic total order. As a special case, we deduce the finite length property of the Rado graph using both methods. We also describe some connections with function spaces, weighted register automata, and orbit-finite systems of linear equations.

BibTeX

  @InProceedings{YangBojanczykKlin-TheFiniteLengthProp,
    author = 	 {Jingjie Yang and Mikołaj Bojańczyk and Bartek Klin},
    title = 	 {The Finite Length Property of the Rado Graph and Friends},
    booktitle =  {Proceedings of the Forty-First Annual Symposium on Logic in Computer Science (LICS 2026)},
    year =	 {2026},
    month =	 {July}, 
    pages =      {82:1--82:27},
    location =   {Lisbon, Portugal}, 
    publisher =	 {Schloss Dagstuhl -- Leibniz-Zentrum für Informatik},
    doi =        {10.4230/LIPIcs.LICS.2026.82}
  }