Introduction to Incompleteness From Gödel's Theorems to Forcing and the Continuum Hypothesis /
Incompleteness is a fascinating phenomenon at the intersection of mathematical foundations, computer science, and epistemology that places a limit on what is provable. However, despite its importance, it is often overlooked in the mathematics curricula because it is difficult to teach. This book aim...
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| Format: | Elektronski eKnjiga |
| Jezik: | angleščina |
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Springer Nature Switzerland : Imprint: Birkhäuser,
2024.
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| Izdaja: | 1st ed. 2024. |
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| Online dostop: | https://doi.org/10.1007/978-3-031-64217-3 |
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Kazalo:
- Part 1: Godel's Theorems
- Formal Axiomatic Systems
- Peano Arithmetic and Recursive Functions
- Godel's Incompleteness Theorems
- Structures, Models, and Satisfaction
- Completeness and Compactness Theorems
- Completeness and Peano Arithmetic
- The Lucas-Penrose Arguments
- Part II: Incompleteness in arithmetic and set theory
- Incompleteness in Finite Combinatorics
- Consistency of PA and E0 Induction
- Set Theory
- Independence of CH--forcing
- Independence of CH--forcing CH and -CH.