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PopularA Problem Course in Mathematical Logic
Year: 2003
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A Problem Course in Mathematical Logic is intended to serve as the text for an introduction to mathematical logic for undergraduates with some mathematical sophistication. It supplies definitions, statements of results, and problems, along with some explanations, examples, and hints. The idea is for the students, individually or in groups, to learn the material by solving the problems and proving the results for themselves. The book should do as the text for a course taught using the modified Moore-method.
The material and its presentation are pretty stripped-down and it will probably be desirable for the instructor to supply further hints from time to time or to let the students consult other sources. Various concepts and and topics that are often covered in introductory mathematical logic or computability courses are given very short shrift or omitted entirely, among them normal forms, definability, and model theory.
Parts I and II, Propositional Logic and First-Order Logic respectively, cover the basics of these topics through the Soundness, Completeness, and Compactness Theorems, plus a little on applications of the Compactness Theorem. They could be used for a one-term course on these subjects. Part III, Computability, covers the basics of computability using Turing machines and recursive functions; it could be used as the basis of a one-term course. Part IV, Incompleteness, is concerned with proving the Gödel Incompleteness Theorems. With the omission of some topics from Part III which are not needed to prove the results in Part IV, Parts III and IV could be used for a one-term course for students who know the contents of Part II already.
A Problem Course in Mathematical Logic is intended to serve as the text for an introduction to mathematical logic for undergraduates with some mathematical sophistication. It supplies definitions, statements of results, and problems, along with some explanations, examples, and hints. The idea is for the students, individually or in groups, to learn the material by solving the problems and proving the results for themselves. The book should do as the text for a course taught using the modified Moore-method.
The material and its presentation are pretty stripped-down and it will probably be desirable for the instructor to supply further hints from time to time or to let the students consult other sources. Various concepts and and topics that are often covered in introductory mathematical logic or computability courses are given very short shrift or omitted entirely, among them normal forms, definability, and model theory.
Parts I and II, Propositional Logic and First-Order Logic respectively, cover the basics of these topics through the Soundness, Completeness, and Compactness Theorems, plus a little on applications of the Compactness Theorem. They could be used for a one-term course on these subjects. Part III, Computability, covers the basics of computability using Turing machines and recursive functions; it could be used as the basis of a one-term course. Part IV, Incompleteness, is concerned with proving the Gödel Incompleteness Theorems. With the omission of some topics from Part III which are not needed to prove the results in Part IV, Parts III and IV could be used for a one-term course for students who know the contents of Part II already.