Gerhard Gentzen (gentzen)
Cited in the following articles
Weyl, Gödel and the Grundlagenstreit, The Formalization of Arguments: An Overview, Reflective Equilibrium on the Fringe, Holistic Inferential Criteria of Adequate FormalizationContributions to Philosophie.ch
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Bibliography
Gentzen, Gerhard. 1932. “Über die Existenz unabhängiger Axiomensysteme zu unendlichen Satzsystemen.” Mathematische Annalen 107: 329–350.
Gentzen, Gerhard. 1935. “Untersuchungen über das logische Schliessen.” Mathematische Zeitschrift 39: 176–210, 405–431. Republished as Gentzen (1969a), doi:10.1007/BF01201353.
Gentzen, Gerhard. 1936a. “Die Widerspruchsfreiheit der reinen Zahlentheorie.” Mathematische Annalen 112: 493–565.
Gentzen, Gerhard. 1936b. “Die Widerspruchsfreiheit der Stufenlogik.” Mathematische Zeitschrift 41: 357–366.
Gentzen, Gerhard. 1938a. “Die gegenwärtige Lage in der mathematischen Grundlagenforschung.” Forschungen zur Logik und zur Grundlegung der exakten Wissenschaften 4: 5–18.
Gentzen, Gerhard. 1938b. “Neue Fassung des Widerspruchsfreiheitsbeweises für die reine Zahlentheorie.” Forschungen zur Logik und zur Grundlegung der exakten Wissenschaften 4: 19–44.
Gentzen, Gerhard. 1943. “Beweisbarkeit und Unbeweisbarkeit von Anfangsfällen der transfiniten Induktion in der reinen Zahlentheorie.” Mathematische Annalen 119(1): 140–161.
Gentzen, Gerhard. 1954. “Zusammenfassung von mehreren vollständigen Induktionen zu einer einzigen.” Archiv für mathematische Logik und Grundlagenforschung 2(1): 81–93.
Gentzen, Gerhard. 1955. Recherches sur la déduction logique. Paris: Presses Universitaires de France. Traduction de Gentzen (1935) par Robert Feys et Jean Ladrière.
Gentzen, Gerhard. 1965. “Investigations into Logical Deduction II.” American Philosophical Quarterly 2(3): 204–218. Originally published in 1935, translated by M.E. Szabo.
Gentzen, Gerhard. 1969a. Untersuchungen über das logische Schliessen. Darmstadt: Wissenschaftliche Buchgesellschaft.
Gentzen, Gerhard. 1969b. The Collected Papers of Gerhard Gentzen. Studies in Logic and the Foundations of Mathematics n. 55. Amsterdam: North-Holland Publishing Co. Edited by M.E. Szabo.
Gentzen, Gerhard. 1969c. “On the Existence of Independent Axiom Systems for Infinite Sentence Systems.” in The Collected Papers of Gerhard Gentzen, pp. 29–52. Studies in Logic and the Foundations of Mathematics n. 55. Amsterdam: North-Holland Publishing Co. Translation of Gentzen (1932) by M.E. Szabo.
Gentzen, Gerhard. 1969d. “On the Relation Between Intuitionist and Classical Arithmetic.” in The Collected Papers of Gerhard Gentzen, pp. 53–67. Studies in Logic and the Foundations of Mathematics n. 55. Amsterdam: North-Holland Publishing Co. Translation by M.E. Szabo, publication of the original (1933) as Gentzen (1974b).
Gentzen, Gerhard. 1969e. “Investigations into Logical Deduction.” in The Collected Papers of Gerhard Gentzen, pp. 68–131. Studies in Logic and the Foundations of Mathematics n. 55. Amsterdam: North-Holland Publishing Co. Translation of Gentzen (1935) by M.E. Szabo.
Gentzen, Gerhard. 1969f. “The Consistency of Elementary Number Theory.” in The Collected Papers of Gerhard Gentzen, pp. 132–213. Studies in Logic and the Foundations of Mathematics n. 55. Amsterdam: North-Holland Publishing Co. Translation of Gentzen (1936a) by M.E. Szabo.
Gentzen, Gerhard. 1969g. “The Consistency of the Simple Theory of Types.” in The Collected Papers of Gerhard Gentzen, pp. 214–222. Studies in Logic and the Foundations of Mathematics n. 55. Amsterdam: North-Holland Publishing Co. Translation of Gentzen (1936b) by M.E. Szabo.
Gentzen, Gerhard. 1969h. “The Concept of Infinity in Mathematics.” in The Collected Papers of Gerhard Gentzen, pp. 223–233. Studies in Logic and the Foundations of Mathematics n. 55. Amsterdam: North-Holland Publishing Co. Translation of Gentzen (1936c) by M.E. Szabo.
Gentzen, Gerhard. 1969i. “The Present State of Research into the Foundations of Mathematics.” in The Collected Papers of Gerhard Gentzen, pp. 234–251. Studies in Logic and the Foundations of Mathematics n. 55. Amsterdam: North-Holland Publishing Co. Translation of Gentzen (1938a) by M.E. Szabo.
Gentzen, Gerhard. 1969j. “New Version of the Consistency Proof for Elementary Number Theory.” in The Collected Papers of Gerhard Gentzen, pp. 252–286. Studies in Logic and the Foundations of Mathematics n. 55. Amsterdam: North-Holland Publishing Co. Translation of Gentzen (1938b) by M.E. Szabo.
Gentzen, Gerhard. 1969k. “Provability and Nonprovability of Restricted Transfinite Induction in Elementary Number Theory.” in The Collected Papers of Gerhard Gentzen, pp. 287–308. Studies in Logic and the Foundations of Mathematics n. 55. Amsterdam: North-Holland Publishing Co. Translation of Gentzen (1943) by M.E. Szabo.
Gentzen, Gerhard. 1969l. “Fusion of Several Complete Inductions.” in The Collected Papers of Gerhard Gentzen, pp. 309–310. Studies in Logic and the Foundations of Mathematics n. 55. Amsterdam: North-Holland Publishing Co. Translation of Gentzen (1954) by M.E. Szabo.
Gentzen, Gerhard. 1974a. “Der erste Widerspruchsfreiheitsbeweis für die klassische Zahlentheorie.” Archiv für mathematische Logik und Grundlagenforschung 16: 97–118. Published postumously by Paul Bernays.
Gentzen, Gerhard. 1974b. “Über das Verhältnis zwischen intuitionistischer und klassischer Arithmetik.” Archiv für mathematische Logik und Grundlagenforschung 16: 119–132. Published postumously by Paul Bernays.