An Invitation to Mathematical Logic
In addition to covering the essentials, the author’s intention in writing this text is to entice the reader to further study mathematical logic. There is no current “standard text” for a first graduate course in mathematical logic and this book will fill that gap. While there is more material than c...
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| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
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Springer Nature Switzerland : Imprint: Springer,
2024.
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| Ausgabe: | 1st ed. 2024. |
| Schriftenreihe: | Graduate Texts in Mathematics,
301 |
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| Online-Zugang: | https://doi.org/10.1007/978-3-031-55368-4 |
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Inhaltsangabe:
- Introduction
- I. Truth and Proof
- 1 Languages, Structures and Theories
- 2 Embeddings and Substructures
- 3 Formal Proofs
- 4 Gödel's Completeness Theorem
- II. Elements of Model Theory
- 5 Compactness and Complete Theories
- 6 Ultraproducts
- 7 Quantifier Elimination
- 8 Model Theory of the Real Field
- III. Computability
- 9 Models of Computation
- 10 Universal Machines and Undecidability
- 11 Computably Enumerable and Arithmetic Sets
- 12 Turing Reducibility
- IV. Arithmetic and Incompleteness.-13 Gödel's Incompleteness Theorems
- 14 Hilbert’s 10th Problem
- 15 Peano Arithmetic and ϵ0
- 16 Models of Arithmetic and Independence Results. - Appendices
- A Set Theory. - B Unique Readability. - C Real Algebra. -Bibliography. - Index.