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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100 | 1 | |a Heinzmann, Gerhard. | |
245 | 1 | 0 | |a Paul Lorenzen -- Mathematician and Logician. |
250 | |a 1st ed. | ||
264 | 1 | |a Cham : |b Springer International Publishing AG, |c 2021. | |
264 | 4 | |c ©2021. | |
300 | |a 1 online resource (274 pages) | ||
336 | |a text |b txt |2 rdacontent | ||
337 | |a computer |b c |2 rdamedia | ||
338 | |a online resource |b cr |2 rdacarrier | ||
490 | 1 | |a Logic, Epistemology, and the Unity of Science Series ; |v v.51 | |
505 | 0 | |a 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. | |
505 | 8 | |a 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. | |
505 | 8 | |a 10 The correspondence between Hasse and Lorenzen, 1953-1963 -- 11 The correspondence between Aubert and Lorenzen, 1978-1979 -- References. | |
588 | |a Description based on publisher supplied metadata and other sources. | ||
590 | |a Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. | ||
655 | 4 | |a Electronic books. | |
700 | 1 | |a Wolters, Gereon. | |
776 | 0 | 8 | |i Print version: |a Heinzmann, Gerhard |t Paul Lorenzen -- Mathematician and Logician |d Cham : Springer International Publishing AG,c2021 |z 9783030658236 |
797 | 2 | |a ProQuest (Firm) | |
830 | 0 | |a Logic, Epistemology, and the Unity of Science Series | |
856 | 4 | 0 | |u https://ebookcentral.proquest.com/lib/oeawat/detail.action?docID=6707454 |z Click to View |