Mathematical Logic by Heinz-Dieter Ebbinghaus
What is a mathematical proof? How can proofs be justified? Are there limitations to provability? To what extent can machines carry out mathe- matical proofs? Only in this century has there been success in obtaining substantial and satisfactory answers. The present book contains a systematic discussion of these results. The investigations are centered around first-order logic. Our first goal is Godel's completeness theorem, which shows that the con- sequence relation coincides with formal provability: By means of a calcu- lus consisting of simple formal inference rules, one can obtain all conse- quences of a given axiom system (and in particular, imitate all mathemat- ical proofs). A short digression into model theory will help us to analyze the expres- sive power of the first-order language, and it will turn out that there are certain deficiencies. For example, the first-order language does not allow the formulation of an adequate axiom system for arithmetic or analysis. On the other hand, this difficulty can be overcome--even in the framework of first-order logic-by developing mathematics in set-theoretic terms. We explain the prerequisites from set theory necessary for this purpose and then treat the subtle relation between logic and set theory in a thorough manner.
“This newest edition has been reclassified, fittingly, as a graduate text, and it is admirably suited to that role… Those who are already well-versed in logic will find this text to be a valuable reference and a strong resource for teaching at the graduate level, while those who are new to the field will come to know not only how mathematical logic is studied but also, perhaps more importantly, why.” (Stephen Walk, MAA Reviews, January 6, 2023)
Heinz-Dieter Ebbinghaus is Professor Emeritus at the Mathematical Institute of the University of Freiburg. His work spans fields in logic, such as model theory and set theory, and includes historical aspects.
J�rg Flum is Professor Emeritus at the Mathematical Institute of the University of Freiburg. His research interests include mathematical logic, finite model theory, and parameterized complexity theory.
Wolfgang Thomas is Professor Emeritus at the Computer Science Department of RWTH Aachen University. His research interests focus on logic in computer science, in particular logical aspects of automata theory.| SKU | Unavailable |
| ISBN 13 | 9783030738419 |
| ISBN 10 | 3030738418 |
| Title | Mathematical Logic |
| Author | Heinz-Dieter Ebbinghaus |
| Series | Graduate Texts In Mathematics |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | Springer Nature Switzerland AG |
| Year published | 2022-05-30 |
| Number of pages | 304 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |