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.

Autorentext
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.

Inhalt
Well, Better, and in-between.- The Categorical Structure of Well-Quasi Orders.- On Kriz's Theorem.- On the Width of FAC Orders, a Somewhat Rediscovered Notion.- Preliminary Well-quasi Orders in the Study of Hierarchies and Reducibilities.- The Ideal Approach to Computing Closed Subsets in Well-Quasi-Orderings.- Well-Quasi Orders and Regularity.- Well Quasi Ordering and Embeddability of Relational Structures.- A Functional Interpretation of Zorn's Lemma and its Application in Well-Quasi-Order Theory.- The Reverse Mathematics of wqos and bqos.- Well-partial Ordering and the Maximal Order Type.- TBC.- The Worlds of Well-Partial-Orders and Ordinal Notation systems.- Bounds for the Strength of the Graph Minor Theorem.