Gerald E. Sacks – författare

The description for this book, Degrees of Unsolvability. (AM-55), will be forthcoming.

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the second publication in the Perspectives in Logic series, is an almost self-contained introduction to higher recursion theory, in which the reader is only assumed to know the basics of classical recursion theory. The book is divided into four parts: hyperarithmetic sets, metarecursion, α-recursion, and E-recursion. This text is essential reading for all researchers in the field.

The courses given at the 1st CIME Summer school of 1988 dealt with the main areas on the borderline between applied logic and theoretical computer science. These courses are recorded here in five expository papers and cover such topics as isomorphism conjecture and its generalization, intuitionistic logic and PROLOG programming.

These proceedings contain research and survey papers from many subfields of recursion theory, with emphasis on degree theory, in particular the development of frameworks for current techniques in this field. Other topics covered include computational complexity theory, generalized recursion theory, proof theoretic questions in recursion theory and recursive mathematics.

This book contains the material for a first course in pure model theory with applications to differentially closed fields. Topics covered in this book include saturated model criteria for model completeness and elimination of quantifiers; Morley rank and degree of element types; categoricity in power; two-cardinal theorems; existence and uniqueness of prime model extensions of substructures of models of totally transcendental theories; and homogeneity of models of ϖ1-categorical theories.

The author selects 23 of his papers in mathematical logic that pursue definability via priority, forcing, compactness and fine structure applied to classical recursion, hyperarithmetic sets, recursion in objects of finite type, measure, models and E-recursion. His general introduction provides a chronology both personal and technical.