Well-Quasi Orders in Computation, Logic, Language and Reasoning: A Unifying Concept of Proof Theory, Automata Theory, Formal Languages and Descriptive Set Theory

Description

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. Front Matter ....Pages i-x Well, Better and In-Between (Raphaël Carroy, Yann Pequignot)....Pages 1-27 On Ordinal Invariants in Well Quasi Orders and Finite Antichain Orders (Mirna Džamonja, Sylvain Schmitz, Philippe Schnoebelen)....Pages 29-54 The Ideal Approach to Computing Closed Subsets in Well-Quasi-orderings (Jean Goubault-Larrecq, Simon Halfon, Prateek Karandikar, K. Narayan Kumar, Philippe Schnoebelen)....Pages 55-105 Strong WQO Tree Theorems (Lev Gordeev)....Pages 107-125 Well Quasi-orderings and Roots of Polynomials in a Hahn Field (Julia F. Knight, Karen Lange)....Pages 127-144 Upper Bounds on the Graph Minor Theorem (Martin Krombholz, Michael Rathjen)....Pages 145-159 Recent Progress on Well-Quasi-ordering Graphs (Chun-Hung Liu)....Pages 161-188 The Reverse Mathematics of wqos and bqos (Alberto Marcone)....Pages 189-219 Well Quasi-orders and the Functional Interpretation (Thomas Powell)....Pages 221-269 Well-Quasi Orders and Hierarchy Theory (Victor Selivanov)....Pages 271-319 A Combinatorial Bound for a Restricted Form of the Termination Theorem (Silvia Steila)....Pages 321-338 A Mechanized Proof of Higman’s Lemma by Open Induction (Christian Sternagel)....Pages 339-350 Well-Partial Orderings and their Maximal Order Types ( Diana Schmidt)....Pages 351-391