Ebook: Logical Methods: In Honor of Anil Nerode’s Sixtieth Birthday

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.

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Content:
Front Matter....Pages i-xiv
The Work of Anil Nerode: A Retrospective....Pages 1-91
Embedding Distributive Lattices Preserving 1 below a Nonzero Recursively Enumerable Turing Degree....Pages 92-129
Prime Isols and the Theorems of Fermat and Wilson....Pages 130-142
Problem Solving Strategies for the Derivation of Programs....Pages 143-161
Effective Real Dynamics....Pages 162-177
An integer lattice arising in the model theory of wreath products....Pages 178-193
Undecidability and Definability for Parametrized Polynomial Time m-Reducibilities....Pages 194-221
Extracting programs from proofs by an extension of the Curry-Howard process....Pages 222-288
A Bird’s-Eye View of Twilight Combinatorics....Pages 289-313
Effectively and Noneffectively Nowhere Simple Subspaces....Pages 314-351
Index Sets in Recursive Combinatorics....Pages 352-385
Computability in Unitary Representations of Compact Groups....Pages 386-421
Recursive Properties of Intervals of Recursive Linear Orders....Pages 422-437
Algorithmic Stability of Models....Pages 438-466
The Combinatorics of the Friedberg-Muchnick Theorem....Pages 467-489
Partial Automata and Finitely Generated Congruences: An Extension of Nerode’s Theorem....Pages 490-511
Minimal Pair Constructions and Iterated Trees of Strategies....Pages 512-554
Intuitionistic L....Pages 555-571
n-Recursive Linear Orders without (n+1)-Recursive Copies....Pages 572-592
Multiple Agent Autonomous Control A Hybrid Systems Architecture....Pages 593-623
Distributed Concurrent Programs as Strategies in Games....Pages 624-653
Dempster-Shafer Logic Programs and Stable Semantics....Pages 654-704
Who Put The “Back” In Back-And-Forth?....Pages 705-712
Polynomial Time Categoricity and Linear Orderings....Pages 713-746
The Disjunction and Numerical Existence Properties for Intuitionistic Analysis....Pages 747-781
On the strength of Fra?ss?’s conjecture....Pages 782-813
Back Matter....Pages 815-816

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Content:
Front Matter....Pages i-xiv
The Work of Anil Nerode: A Retrospective....Pages 1-91
Embedding Distributive Lattices Preserving 1 below a Nonzero Recursively Enumerable Turing Degree....Pages 92-129
Prime Isols and the Theorems of Fermat and Wilson....Pages 130-142
Problem Solving Strategies for the Derivation of Programs....Pages 143-161
Effective Real Dynamics....Pages 162-177
An integer lattice arising in the model theory of wreath products....Pages 178-193
Undecidability and Definability for Parametrized Polynomial Time m-Reducibilities....Pages 194-221
Extracting programs from proofs by an extension of the Curry-Howard process....Pages 222-288
A Bird’s-Eye View of Twilight Combinatorics....Pages 289-313
Effectively and Noneffectively Nowhere Simple Subspaces....Pages 314-351
Index Sets in Recursive Combinatorics....Pages 352-385
Computability in Unitary Representations of Compact Groups....Pages 386-421
Recursive Properties of Intervals of Recursive Linear Orders....Pages 422-437
Algorithmic Stability of Models....Pages 438-466
The Combinatorics of the Friedberg-Muchnick Theorem....Pages 467-489
Partial Automata and Finitely Generated Congruences: An Extension of Nerode’s Theorem....Pages 490-511
Minimal Pair Constructions and Iterated Trees of Strategies....Pages 512-554
Intuitionistic L....Pages 555-571
n-Recursive Linear Orders without (n+1)-Recursive Copies....Pages 572-592
Multiple Agent Autonomous Control A Hybrid Systems Architecture....Pages 593-623
Distributed Concurrent Programs as Strategies in Games....Pages 624-653
Dempster-Shafer Logic Programs and Stable Semantics....Pages 654-704
Who Put The “Back” In Back-And-Forth?....Pages 705-712
Polynomial Time Categoricity and Linear Orderings....Pages 713-746
The Disjunction and Numerical Existence Properties for Intuitionistic Analysis....Pages 747-781
On the strength of Fra?ss?’s conjecture....Pages 782-813
Back Matter....Pages 815-816
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