Well-Quasi Orders in Computation, Logic, Language and Reasoning

A Unifying Concept of Proof Theory, Automata Theory, Formal Languages and Descriptive Set Theory

  • Peter M. Schuster
  • Monika Seisenberger
  • Andreas Weiermann

Part of the Trends in Logic book series (TREN, volume 53)

Table of contents

  1. Front Matter
    Pages i-x
  2. Raphaël Carroy, Yann Pequignot
    Pages 1-27
  3. Mirna Džamonja, Sylvain Schmitz, Philippe Schnoebelen
    Pages 29-54
  4. Jean Goubault-Larrecq, Simon Halfon, Prateek Karandikar, K. Narayan Kumar, Philippe Schnoebelen
    Pages 55-105
  5. Lev Gordeev
    Pages 107-125
  6. Julia F. Knight, Karen Lange
    Pages 127-144
  7. Martin Krombholz, Michael Rathjen
    Pages 145-159
  8. Chun-Hung Liu
    Pages 161-188
  9. Alberto Marcone
    Pages 189-219
  10. Victor Selivanov
    Pages 271-319

About this book


This book bridges the gaps between logic, mathematics and computer science by delving into the theory of well-quasi orders, also known as wqos. This highly active branch of combinatorics is deeply rooted in and between many fields of mathematics and logic, including proof theory, commutative algebra, braid groups, graph theory, analytic combinatorics, theory of relations, reverse mathematics and subrecursive hierarchies. As a unifying concept for slick finiteness or termination proofs, wqos have been rediscovered in diverse contexts, and proven to be extremely useful in computer science. 

The book introduces readers to the many facets of, and recent developments in, wqos through chapters contributed by scholars from various fields. As such, it offers a valuable asset for logicians, mathematicians and computer scientists, as well as scholars and students.


Well Quasi-order Combinatorics Graph Theory Proof Theory Descriptive Set Theory Maximal Order Type Ordinal Notation System Reverse Mathematics Graph-minor Theorem Termination Proofs constructive mathematics computational content of classical proofs Theorem Proving and Verification discrete mathematics commutative algebra braid groups analytic combinatorics subrecursive hierarchies theory of relations Kriz's Theorem

Editors and affiliations

  • Peter M. Schuster
    • 1
  • Monika Seisenberger
    • 2
  • Andreas Weiermann
    • 3
  1. 1.Dipartimento di InformaticaUniversità degli Studi di VeronaVeronaItaly
  2. 2.Department of Computer ScienceSwansea UniversitySwanseaUK
  3. 3.Vakgroep WiskundeGhent UniversityGhentBelgium

Bibliographic information

  • DOI
  • Copyright Information Springer Nature Switzerland AG 2020
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-30228-3
  • Online ISBN 978-3-030-30229-0
  • Series Print ISSN 1572-6126
  • Series Online ISSN 2212-7313
  • Buy this book on publisher's site