© 2020

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

About the editors

Peter Schuster is an Associate Professor of Mathematical Logic at the University of Verona. After completing both his doctorate and habilitation in mathematics at the University of Munich, he was a Lecturer at the University of Leeds and member of the Leeds Logic Group. Apart from constructive mathematics in general, his principal research interests are in the computational content of classical proofs in abstract algebra and related fields, in which maximum or minimum principles are invoked.

Monika Seisenberger is an Associate Professor of Computer Science at Swansea University. After completing a PhD in the Graduate Programme “Logic in Computer Science” at the LMU Munich she took up a position as research assistant at Swansea University, where she was subsequently appointed lecturer and later programme director. Her research focuses on logic, and on theorem proving and verification.

Andreas Weiermann is a Full Professor of Mathematics at Ghent University. After completing both his doctorate and habilitation in mathematics at the University of Münster, he held postdoctoral positions in Münster and Utrecht and became first an Associate Professor and later Full Professor in Ghent. His research interests include proof theory, theoretical computer science and discrete mathematics.

Bibliographic information

  • Book Title Well-Quasi Orders in Computation, Logic, Language and Reasoning
  • Book Subtitle A Unifying Concept of Proof Theory, Automata Theory, Formal Languages and Descriptive Set Theory
  • Editors Peter M. Schuster
    Monika Seisenberger
    Andreas Weiermann
  • Series Title Trends in Logic
  • Series Abbreviated Title Trends in Logic
  • DOI
  • Copyright Information Springer Nature Switzerland AG 2020
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-030-30228-3
  • Softcover ISBN 978-3-030-30231-3
  • eBook ISBN 978-3-030-30229-0
  • Series ISSN 1572-6126
  • Series E-ISSN 2212-7313
  • Edition Number 1
  • Number of Pages X, 391
  • Number of Illustrations 99 b/w illustrations, 4 illustrations in colour
  • Topics Logic
    Graph Theory
    Mathematical Logic and Formal Languages
    Logic Design
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