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Volumn 147, Issue 1, 2005, Pages 121-170

Dedekind's analysis of number: Systems and axioms

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EID: 24144437368     PISSN: 00397857     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11229-004-6300-9     Document Type: Review
Times cited : (45)

References (86)
  • 4
    • 24144491854 scopus 로고    scopus 로고
    • Paradoxes of the infinite
    • Partial English translation from "Paradoxes of the Infinite" by Donald Stell; in: Ewald 1996, pp. 249-292.
    • Ewald 1996 , pp. 249-292
    • Stell, D.1
  • 8
    • 14644401591 scopus 로고
    • Über die Einführung neuer Funktionen in der Mathematik; Habilitationsvortrag
    • Dedekind, R.: 1854, 'Über die Einführung neuer Funktionen in der Mathematik; Habilitationsvortrag'. In: Dedekind 1932, pp. 428-438.
    • (1854) Dedekind 1932 , pp. 428-438
    • Dedekind, R.1
  • 9
    • 24144448123 scopus 로고    scopus 로고
    • On the introduction of new functions in mathematics
    • English translation "On the introduction of new functions in mathematics" by William Ewald; in Ewald 1996, pp. 754-762.
    • Ewald 1996 , pp. 754-762
    • Ewald, W.1
  • 12
    • 24144475608 scopus 로고    scopus 로고
    • printed in: Dugac 1976, pp. 203-209.
    • Dugac 1976 , pp. 203-209
  • 14
    • 24144498816 scopus 로고    scopus 로고
    • Reprinted in Dedekind 1932, pp. 315-334.
    • Dedekind 1932 , pp. 315-334
  • 15
    • 0011343336 scopus 로고    scopus 로고
    • Continuity and irrational numbers
    • revised by William Ewald
    • English translation "Continuity and irrational numbers" by Wooster W. Beman, revised by William Ewald; in Ewald 1996, pp. 765-779.
    • Ewald 1996 , pp. 765-779
    • Beman, W.W.1
  • 19
    • 24144450612 scopus 로고    scopus 로고
    • printed in: Dugac 1976, pp. 293-309.
    • Dugac 1976 , pp. 293-309
  • 25
    • 24144487808 scopus 로고    scopus 로고
    • revised by William Ewald
    • English translation by Wooster W. Beman, revised by William Ewald, in: Ewald 1996, pp. 787-833.
    • Ewald 1996 , pp. 787-833
    • Beman, W.W.1
  • 27
    • 24144443576 scopus 로고    scopus 로고
    • printed in: Sinaceur 1974, pp. 270-278.
    • Sinaceur 1974 , pp. 270-278
  • 29
    • 24144445960 scopus 로고
    • Cod. Ms. Dedekind III, 1, IV; submitted to, but not published by, the Mathematische Gesellschaft in Hamburg
    • Dedekind, R.: 1890*, Über den Begriff des Unendlichen; Cod. Ms. Dedekind III, 1, IV; submitted to, but not published by, the Mathematische Gesellschaft in Hamburg;
    • (1890) Über den Begriff des Unendlichen
    • Dedekind, R.1
  • 30
    • 24144443576 scopus 로고    scopus 로고
    • printed in: Sinaceur 1974, pp. 259-269.
    • Sinaceur 1974 , pp. 259-269
  • 32
    • 0010821352 scopus 로고
    • Vieweg & Sohn, Braunschweig. Edited by Robert Fricke, Emmy Noether, and Öystein Ore
    • Dedekind, R.: 1932, Gesammelte mathematische Werke, Volume 3; Vieweg & Sohn, Braunschweig. Edited by Robert Fricke, Emmy Noether, and Öystein Ore.
    • (1932) Gesammelte Mathematische Werke , vol.3
    • Dedekind, R.1
  • 33
    • 0003641112 scopus 로고    scopus 로고
    • Cambridge University Press. Translated and introduced by John Stillwell
    • Dedekind, R.: 1996, Theory of algebraic integers; Cambridge University Press. Translated and introduced by John Stillwell.
    • (1996) Theory of Algebraic Integers
    • Dedekind, R.1
  • 38
    • 0039767576 scopus 로고
    • G. Gabriel (ed.), Felix Meiner, Hamburg
    • Frege, G.: 1969, G. Gabriel (ed.), Nachgelassene Schriften; Felix Meiner, Hamburg.
    • (1969) Nachgelassene Schriften
    • Frege, G.1
  • 39
    • 33747715571 scopus 로고
    • Anzeige der Theoria residuorum biquadraticorum, Commentatio secunda
    • 23 April 1831
    • Gauss, C. F.: 1831, 'Anzeige der Theoria residuorum biquadraticorum, Commentatio secunda'; Göttingische gelehrte Anzeigen, 23 April 1831.
    • (1831) Göttingische Gelehrte Anzeigen
    • Gauss, C.F.1
  • 40
    • 24144462665 scopus 로고
    • Reprinted in: Gauss 1863-1929, Vol. 2 (1876), pp. 169-78.
    • (1876) Gauss 1863-1929 , vol.2 , pp. 169-178
  • 41
    • 24144451985 scopus 로고    scopus 로고
    • English translation by William Ewald, in: Ewald 1996, pp. 306-313.
    • Ewald 1996 , pp. 306-313
    • Ewald, W.1
  • 42
    • 0010155384 scopus 로고
    • 12 vols., Königliche Gesellschaft der Wissenschaften, Göttingen, Leipzig, and Berlin
    • Gauss, C. F.: 1863-1929, Werke, 12 vols., Königliche Gesellschaft der Wissenschaften, Göttingen, Leipzig, and Berlin.
    • (1863) Werke
    • Gauss, C.F.1
  • 43
    • 0346800496 scopus 로고
    • The nineteenth-century revolution in mathematical ontology
    • D. Gillies (ed.). Clarendon Press, Oxford
    • Gray, J.: 1992, 'The nineteenth-century revolution in mathematical ontology', in: D. Gillies (ed.). Revolutions in Mathematics, Clarendon Press, Oxford pp. 226-248.
    • (1992) Revolutions in Mathematics , pp. 226-248
    • Gray, J.1
  • 45
    • 24144474360 scopus 로고    scopus 로고
    • reprinted in: Ewald 1996, pp. 375-425.
    • Ewald 1996 , pp. 375-425
  • 48
  • 50
    • 24144451986 scopus 로고    scopus 로고
    • On the concept of number
    • English translation "On the concept of number" by William Ewald, in: Ewald 1996, pp. 1089-1095.
    • Ewald 1996 , pp. 1089-1095
    • Ewald, W.1
  • 51
    • 0001946992 scopus 로고
    • Mathematische Probleme
    • Vortrag, gehalten auf dem internationalen Mathematiker-Kongress zu Paris. 1900
    • Hilbert, D.: 1900b, 'Mathematische Probleme'. Vortrag, gehalten auf dem internationalen Mathematiker-Kongress zu Paris. 1900; Nachrichten der Königlichen Gesellschaft der Wissenschaften zu Göttingen, pp. 253-297.
    • (1900) Nachrichten der Königlichen Gesellschaft der Wissenschaften zu Göttingen , pp. 253-297
    • Hilbert, D.1
  • 52
    • 24144492431 scopus 로고    scopus 로고
    • Mathematical problems
    • Partial translation "Mathematical Problems" by William Ewald, in: Ewald 1996, pp. 1096-1105.
    • Ewald 1996 , pp. 1096-1105
    • Ewald, W.1
  • 54
    • 84858541482 scopus 로고    scopus 로고
    • On the foundations of logic and arithmetic
    • English translation "On the foundations of logic and arithmetic" by Beverly Woodward, in: van Heijenoort 1967, pp. 129-138.
    • Van Heijenoort 1967 , pp. 129-138
    • Woodward, B.1
  • 55
    • 0012805292 scopus 로고
    • Die Grundlegung der elementaren Zahlentheorie
    • Hilbert, D.: 1931, 'Die Grundlegung der elementaren Zahlentheorie'; Mathematische Annalen 104, pp. 485-494.
    • (1931) Mathematische Annalen , vol.104 , pp. 485-494
    • Hilbert, D.1
  • 58
    • 24144448326 scopus 로고    scopus 로고
    • On the concept of number
    • English translation "On the concept of number" by William Ewald, in: Ewald 1996, pp. 947-955.
    • Ewald 1996 , pp. 947-955
    • Ewald, W.1
  • 60
    • 0033246734 scopus 로고    scopus 로고
    • Between Russell and Hilbert: Behmann on the foundations of mathematics
    • Mancosu, P.: 1999, 'Between Russell and Hilbert: Behmann on the foundations of mathematics'; Bulletin of Symbolic Logic 5(3), 303-330.
    • (1999) Bulletin of Symbolic Logic , vol.5 , Issue.3 , pp. 303-330
    • Mancosu, P.1
  • 64
    • 0039777602 scopus 로고
    • The Structuralist view of mathematical objects
    • Parsons, C.: 1990, 'The Structuralist View of Mathematical Objects' Synthese 84, pp. 303-346.
    • (1990) Synthese , vol.84 , pp. 303-346
    • Parsons, C.1
  • 66
    • 0003189377 scopus 로고
    • Sul concetto di numero
    • Peano, G.: 1891, 'Sul concetto di numero'; Rivista di Matematica 1, 87-102 and 256-267.
    • (1891) Rivista di Matematica , vol.1 , pp. 87-102
    • Peano, G.1
  • 67
    • 3142731794 scopus 로고
    • Herbart's Influence on Bernhard Riemann
    • Scholz, E.: 1982, 'Herbart's Influence on Bernhard Riemann'; Historia Mathematica 9, pp. 413-40.
    • (1982) Historia Mathematica , vol.9 , pp. 413-440
    • Scholz, E.1
  • 69
    • 0039671028 scopus 로고
    • Relative consistency and accessible domains
    • Sieg, W.: 1990, 'Relative Consistency and Accessible Domains', Synthese 84, pp. 259-97.
    • (1990) Synthese , vol.84 , pp. 259-297
    • Sieg, W.1
  • 70
    • 0033439938 scopus 로고    scopus 로고
    • Hilbert's programs: 1917-1922
    • Sieg, W.: 1999, 'Hilbert's Programs: 1917-1922'; Bulletin of Symbolic Logic 5, 1-44.
    • (1999) Bulletin of Symbolic Logic , vol.5 , pp. 1-44
    • Sieg, W.1
  • 71
    • 24144481315 scopus 로고    scopus 로고
    • Reductive structuralism
    • Carnegie Mellon University, Department of Philosophy
    • Sieg, W.: 2000, 'Reductive Structuralism'; Technical Report CMU-PHIL-108, Carnegie Mellon University, Department of Philosophy.
    • (2000) Technical Report , vol.CMU-PHIL-108
    • Sieg, W.1
  • 74
    • 24144500895 scopus 로고
    • L'infini et les nombres - Commentaires de R. Dedekind à 'Zahlen' - La correspondance avec Keferstein
    • Sinaceur, M.-A.: 1974, 'L'infini et les nombres - Commentaires de R. Dedekind à 'Zahlen' - La correspondance avec Keferstein'; Revue d'histoire des sciences 27, 251-278.
    • (1974) Revue d'Histoire des Sciences , vol.27 , pp. 251-278
    • Sinaceur, M.-A.1
  • 75
    • 24144491206 scopus 로고
    • Logos, logic, and logistiké: Some philosophical remarks on nineteenth-century transformation of mathematics
    • William Aspray and Philip Kitcher (eds.), University of Minnesota, Minneapolis
    • Stein, H.: 1988, 'Logos, Logic, and Logistiké: Some Philosophical Remarks on Nineteenth-Century Transformation of Mathematics' in: William Aspray and Philip Kitcher (eds.), History and Philosophy of Modern Mathematics, pp. 238-259. University of Minnesota, Minneapolis.
    • (1988) History and Philosophy of Modern Mathematics , pp. 238-259
    • Stein, H.1
  • 78
    • 24144436247 scopus 로고
    • Critical notice: Charles Parsons' mathematics in philosophy
    • Tait, W.: 1986, 'Critical Notice: Charles Parsons' Mathematics in Philosophy', Philosophy of Science 53, 588-607.
    • (1986) Philosophy of Science , vol.53 , pp. 588-607
    • Tait, W.1
  • 79
    • 24144469257 scopus 로고    scopus 로고
    • Frege versus Cantor and Dedekind: On the concept of number
    • Mathias Schirn (ed.), DeGruyter, Berlin
    • Tait, W.: 1996, 'Frege versus Cantor and Dedekind: On the Concept of Number' in: Mathias Schirn (ed.), Frege: Importance and Legacy, pp. 70-113. DeGruyter, Berlin.
    • (1996) Frege: Importance and Legacy , pp. 70-113
    • Tait, W.1
  • 80
    • 0001811763 scopus 로고
    • Sur les ensembles finis
    • Tarski, A.: 1924, 'Sur les ensembles finis'; Fundamenta Mathematica 6, 45-95.
    • (1924) Fundamenta Mathematica , vol.6 , pp. 45-95
    • Tarski, A.1
  • 84
    • 34250964560 scopus 로고
    • Neuer Beweis für die Möglichkeit einer Wohlordnung
    • Zermelo, E.: 1908, 'Neuer Beweis für die Möglichkeit einer Wohlordnung'; Mathematische Annalen 59, 107-28;
    • (1908) Mathematische Annalen , vol.59 , pp. 107-128
    • Zermelo, E.1
  • 85
  • 86
    • 84947170069 scopus 로고
    • Über die Grundlagen der Arithmetik
    • Roma, 6-11 Aprile 1908, Rome, Academia dei Lincei
    • Zermelo, E.: 1908*, 'Über die Grundlagen der Arithmetik'; in: Atti del IV. Congresso internazionale dei matematici, Roma, 6-11 Aprile 1908, pp. 8-11; Rome, Academia dei Lincei.
    • (1908) Atti del IV. Congresso Internazionale dei Matematici , pp. 8-11
    • Zermelo, E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.