Internal logic : foundations of mathematics from Kronecker to Hilbert /
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht ; Boston :
Kluwer Academic Publishers,
©2002.
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| Series: | Synthese library ;
v. 310. |
| Subjects: |
Table of Contents:
- Chapter 1.. Introduction: Foundations of Mathematics
- 1.. Introduction
- 2.. Philosophy of mathematics and foundational research
- 3.. Mother-theories
- 4.. Mathematical logic
- 5.. theory of mathematical practice
- 6.. Indefinite and indeterminate as foundational concepts
- 7.. Conclusion: The internal logic of polynomial arithmetic
- Chapter 2.. From Hilbert to Kronecker
- 1.. Introduction: Metamathematics
- 2.. Arithmetic
- 3.. Algebra
- 4.. Logic
- 5.. Elliptic functions
- 6.. Kronecker's programme
- 7.. Conclusion: The arithmetization programme
- Chapter 3.. Consistency of Arithmetic Revisited
- 1.. Introduction
- 2.. Finitism
- 3.. Fermat's descent
- 4.. Logic
- 5.. polynomial setting
- 6.. Internal and external consistency of arithmetic
- 7.. Conclusion
- Chapter 4.. Internal Consistency of Arithmetic with Infinite Descent
- ^
- 4.. Modular logic
- 5.. Arithmetic
- 6.. Complexity
- 7.. Conclusion.