Paul Lorenzen -- Mathematician and Logician.
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Superior document: | Logic, Epistemology, and the Unity of Science Series ; v.51 |
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TeilnehmendeR: | |
Place / Publishing House: | Cham : : Springer International Publishing AG,, 2021. ©2021. |
Year of Publication: | 2021 |
Edition: | 1st ed. |
Language: | English |
Series: | Logic, Epistemology, and the Unity of Science Series
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Online Access: | |
Physical Description: | 1 online resource (274 pages) |
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Table of Contents:
- Intro
- Preface
- Contents
- List of Contributors
- 1 Paul Lorenzens Weg von der Mathematik zur Philosophie - Persönliche Erinnerungen
- 2 Operation and Predicativity: Lorenzen's Approach to Arithmetic
- 1 Introduction
- 2 The main philosophical considerations
- 3 The construction of the natural and the real numbers
- 4 A short outlook on predicative mathematics
- References
- 3 Conceptions of Infinity and Set in Lorenzen's Operationist System
- 1 Introduction
- 2 Operationism and the foundational crisis
- 3 Elimination of the classical notion of set
- 4 The question of infinity
- 4.1 A shift in focus
- 4.2 Constructs and infinity
- 4.3 Rejection of actual infinity
- 5 Conclusion and outlook
- References
- 4 Lorenzen and Constructive Mathematics
- Introduction
- 1 Lorenzen's analysis of Gentzen's work
- 1.1 The consistency proof
- 1.2 The inversion principle
- 1.3 Distributive lattices and entailment relations
- 2 Proof-theoretic analysis of point-free spaces
- 3 Measure theory
- 3.1 Borel subsets of Cantor space
- 3.2 Borel's measure problem
- 3.3 An inductive solution of Borel's measure problem
- 4 Game semantics
- References
- 5 Lorenzen between Gentzen and Schütte
- 1 Introduction: Hilbert's Programme after Gentzen
- 2 Lorenzen's consistency proof for ramified type theory (without reducibility)
- 3 Gentzen, Bernays, Schütte
- 4 Digression: Lorenzen's 1951 Zeitschrift paper
- 5 Conclusion
- References
- 6 Syntax for Semantics: Krull's Maximal Ideal Theorem
- 1 Introduction
- 2 Maximal ideals
- 3 Entailment relations
- 4 Krull's theorem without choice
- 5 Applications
- Acknowledgements
- References
- 7 Regular Entailment Relations
- Introduction
- 1 General properties of regular entailment relations
- 2 Another presentation of regular entailment relations
- 3 Equivariant systems of ideals.
- 4 Regularisation of an equivariant system of ideals
- 5 A constructive version of the Lorenzen-Clifford-Dieudonné Theorem
- 6 Prüfer's definition of the regularisation
- 7 The l-group structure in the noncommutative case
- 8 Examples
- Acknowledgements
- References
- 8 Connecting Sequent Calculi with Lorenzen-Style Dialogue Games
- 1 Introduction
- 2 Some sequent calculi
- 3 Two different information extraction games
- 4 Relating games and calculi
- 5 Lorenzen-style games?
- 6 Game variants for other substructural calculi
- 7 Conclusion - an extended research agenda
- References
- 9 Lorenzen's Reshaping of Krull's Fundamentalsatz for Integral Domains (1938-1953)
- 1 Introduction
- 2 Krull 1930: a first attempt at introducing valuations for an integral domain
- 3 Krull 1932: the Fundamentalsatz for integral domains
- 4 Krull 1936a: the computational content of the Fundamentalsatz
- 5 Lorenzen 1939: the Fundamentalsatz for preordered cancellative monoids
- 5.1 Systems of ideals
- 5.2 Ideals in a lattice-preordered group
- 5.3 Transfer to the system of t-ideals
- 6 Lorenzen 1950: the Fundamentalsatz without valuations
- 7 Lorenzen 1952: the Fundamentalsatz for semilattice domains
- 8 Lorenzen 1953: the Fundamentalsatz for integral domains as an embedding into a super-l-group
- 9 A letter from Krull to Scholz from 1953: the well-ordering theorem
- References
- 10 Lorenzen's Correspondence with Hasse, Krull, and Aubert, Together with Some Relevant Documents
- 1 Synopsis
- 2 The correspondence between Krull and Lorenzen, 1938
- 3 The reports on Lorenzen's thesis
- 4 The correspondence between Hasse and Lorenzen, 1938-1942
- 6 The correspondence between Krull and Lorenzen, 1943-1944
- 7 A postcard from Lorenzen to Hasse, 1945
- 8 Documents relating to Lorenzen's career, 1945-1946
- 9 A letter from Krull to Scholz, 1953.
- 10 The correspondence between Hasse and Lorenzen, 1953-1963
- 11 The correspondence between Aubert and Lorenzen, 1978-1979
- References.