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

Springer Nature, Jan 1, 2020 - Philosophy - 391 pages

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.

Contents

• Well Better and InBetween: 1
• On Ordinal Invariants in Well Quasi Orders and Finite Antichain Orders: 29
• The Ideal Approach to Computing Closed Subsets in WellQuasiorderings: 55
• Strong WQO Tree Theorems: 107
• Well Quasiorderings and Roots of Polynomials in a Hahn Field: 127
• Upper Bounds on the Graph Minor Theorem: 145
• Recent Progress on WellQuasiordering Graphs: 161
• The Reverse Mathematics of wqos and bqos: 189
• Well Quasiorders and the Functional Interpretation: 221
• WellQuasi Orders and Hierarchy Theory: 271
• A Combinatorial Bound for a Restricted Form of the Termination Theorem: 321
• A Mechanized Proof of Higmans Lemma by Open Induction: 339
• WellPartial Orderings and their Maximal Order Types: 351

About the author

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

• Title: Well-Quasi Orders in Computation, Logic, Language and Reasoning: A Unifying Concept of Proof Theory, Automata Theory, Formal Languages and Descriptive Set Theory; Volume 53 of Trends in Logic
• Editors: Peter M. Schuster, Monika Seisenberger, Andreas Weiermann
• Publisher: Springer Nature, 2020
• ISBN: 3030302296, 9783030302290
• Length: 391 pages
• Subjects: Computers / Computer Architecture; Computers / Logic Design; Mathematics / Combinatorics; Mathematics / Discrete Mathematics; Mathematics / Graphic Methods; Mathematics / Logic; Philosophy / General; Philosophy / Logic