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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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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Physical Description: | 1 online resource (274 pages) |
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Heinzmann, Gerhard. Paul Lorenzen -- Mathematician and Logician. 1st ed. Cham : Springer International Publishing AG, 2021. ©2021. 1 online resource (274 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Logic, Epistemology, and the Unity of Science Series ; v.51 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. Description based on publisher supplied metadata and other sources. Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. Electronic books. Wolters, Gereon. Print version: Heinzmann, Gerhard Paul Lorenzen -- Mathematician and Logician Cham : Springer International Publishing AG,c2021 9783030658236 ProQuest (Firm) Logic, Epistemology, and the Unity of Science Series https://ebookcentral.proquest.com/lib/oeawat/detail.action?docID=6707454 Click to View |
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English |
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author |
Heinzmann, Gerhard. |
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Heinzmann, Gerhard. Paul Lorenzen -- Mathematician and Logician. Logic, Epistemology, and the Unity of Science Series ; 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. |
author_facet |
Heinzmann, Gerhard. Wolters, Gereon. |
author_variant |
g h gh |
author2 |
Wolters, Gereon. |
author2_variant |
g w gw |
author2_role |
TeilnehmendeR |
author_sort |
Heinzmann, Gerhard. |
title |
Paul Lorenzen -- Mathematician and Logician. |
title_full |
Paul Lorenzen -- Mathematician and Logician. |
title_fullStr |
Paul Lorenzen -- Mathematician and Logician. |
title_full_unstemmed |
Paul Lorenzen -- Mathematician and Logician. |
title_auth |
Paul Lorenzen -- Mathematician and Logician. |
title_new |
Paul Lorenzen -- Mathematician and Logician. |
title_sort |
paul lorenzen -- mathematician and logician. |
series |
Logic, Epistemology, and the Unity of Science Series ; |
series2 |
Logic, Epistemology, and the Unity of Science Series ; |
publisher |
Springer International Publishing AG, |
publishDate |
2021 |
physical |
1 online resource (274 pages) |
edition |
1st ed. |
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. |
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9783030658243 9783030658236 |
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QA - Mathematics |
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QA8-10 |
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Electronic books. |
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Electronic books. |
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https://ebookcentral.proquest.com/lib/oeawat/detail.action?docID=6707454 |
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1265405286 |
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Logic, Epistemology, and the Unity of Science Series ; v.51 |
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Logic, Epistemology, and the Unity of Science Series ; v.51 |
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