Logical Methods

The twenty-six papers in this volume reflect the wide and still expanding range of Anil Nerode's work. A conference on Logical Methods was held in honor of Nerode's sixtieth birthday (4 June 1992) at the Mathematical Sciences Institute, Cornell University, 1-3 June 1992. Some of the conference papers are here, but others are from students, co-workers and other colleagues. The intention of the conference was to look forward, and to see the directions currently being pursued, in the development of work by, or with, Nerode. Here is a brief summary of the contents of this book. We give a retrospective view of Nerode's work. A number of specific areas are readily discerned: recursive equivalence types, recursive algebra and model theory, the theory of Turing degrees and r.e. sets, polynomial-time computability and computer science. Nerode began with automata theory and has also taken a keen interest in the history of mathematics. All these areas are represented. The one area missing is Nerode's applied mathematical work relating to the environment. Kozen's paper builds on Nerode's early work on automata. Recursive equivalence types are covered by Dekker and Barback, the latter using directly a fundamental metatheorem of Nerode. Recursive algebra is treated by Ge & Richards (group representations). Recursive model theory is the subject of papers by Hird, Moses, and Khoussainov & Dadajanov, while a combinatorial problem in recursive model theory is discussed in Cherlin & Martin's paper. Cenzer presents a paper on recursive dynamics.

The Work of Anil Nerode: A Retrospective.- Embedding Distributive Lattices Preserving 1 Below A Nonzero Recursively Enumerable Turing Degree.- Prime Isols and the Theorems of Fermat and Wilson.- Problem Solving Strategies for the Derivation of Programs.- Effective Real Dynamics.- An Integer Lattice Arising in the Model Theory of Wreath Products.- Undecidability and Definability for Parametrized Polynomial Time m-Reducibilities.- Extracting Programs from Proofs by an Extension of the Curry-Howard Process.- A Bird's-Eye View of Twilight Combinatorics.- Effectively and Noneffectively Nowhere Simple Subspaces.- Index Sets in Recursive Combinatorics.- Computability in Unitary Representations of Compact Groups.- Recursive Properties of Intervals of Recursive Linear Orders.- Algorithmic Stability of Models.- The Combinatorics of the Friedberg-Muchnick Theorem.- Partial Automata and Finitely Generated Congruences: An Extension of Nerode's Theorem.- Minimal Pair Constructions and Iterated Treesof Strategies.- Intuitionistic L.- n-Recursive Linear Orders Without (n + 1)-Recursive Copies.- Multiple Agent Autonomous Control - A Hybrid Systems Architecture.- Distributed Concurrent Programs as Strategies in Games.- Dempster-Shafer Logic Programs and Stable Semantics.- Who Put the "Back" in Back-and-Forth?.- Polynomial Time Categoricity and Linear Orderings.- The Disjunction and Numerical Existence Properties for Intuitionistic Analysis.- On the Strength of Fraïssé's Conjecture.