Jeffrey B. Remmel – författare

Anil Nerode, Director of the Mathematics Institute at Cornell, USA, is one of the most influential logicians in the world. This volume, published in his honour, contains much new and significant work. The papers in this book are principally concerned with mathematical logic and some of its applications in computing. The book contains papers on recursion theory, intuitionism, computability in group theory, recursive model theory, reverse mathematics and the extraction of programs from proofs. A survey of Nerode's technical achievements over the last 30 years is also included. In particular, the book features papers on new developments in the understanding of the properties of intuitionistic set theory and intuitionistic analysis, the extension of computability in ordinary mathematics pioneered by Marian Boykan Pour-El and Ian Richards, the proof-theoretic strength of a long-standing conjecture of Fraisse and an extension of, and further account of, the Curry-Howard method of extracting programs from logical proofs. The papers in general arose from the conference, "Logical Methods in Mathematics and Computer Science.A Symposium in Honor of Anil Nerode on the Occasion of his Sixtieth Birthday", held at the Mathematical Sciences Institute at Cornell University, from June 1-3, 1992.

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.

Perspicuity is part of proof. If the process by means of which I get a result were not surveyable, I might indeed make a note that this number is what comes out - but what fact is this supposed to confirm for me? I don''t know ''what is supposed to come out'' . . . . 1 -L. Wittgenstein A feasible computation uses small resources on an abstract computa­ tion device, such as a ''lUring machine or boolean circuit. Feasible math­ ematics concerns the study of feasible computations, using combinatorics and logic, as well as the study of feasibly presented mathematical structures such as groups, algebras, and so on. This volume contains contributions to feasible mathematics in three areas: computational complexity theory, proof theory and algebra, with substantial overlap between different fields. In computational complexity theory, the polynomial time hierarchy is characterized without the introduction of runtime bounds by the closure of certain initial functions under safe composition, predicative recursion on notation, and unbounded minimization (S. Bellantoni); an alternative way of looking at NP problems is introduced which focuses on which pa­ rameters of the problem are the cause of its computational complexity and completeness, density and separation/collapse results are given for a struc­ ture theory for parametrized problems (R. Downey and M. Fellows); new characterizations of PTIME and LINEAR SPACE are given using predicative recurrence over all finite tiers of certain stratified free algebras (D.

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.