Beth's nonclassical valuations
Philosophia Scientiae, Tome 3 (1998-1999) no. 4, pp. 279-302.
@article{PHSC_1998-1999__3_4_279_0,
     author = {de Jongh, Dick and van Ulsen, Paul},
     title = {Beth's nonclassical valuations},
     journal = {Philosophia Scientiae},
     pages = {279--302},
     publisher = {\'Editions Kim\'e},
     volume = {3},
     number = {4},
     year = {1998-1999},
     language = {en},
     url = {http://www.numdam.org/item/PHSC_1998-1999__3_4_279_0/}
}
TY  - JOUR
AU  - de Jongh, Dick
AU  - van Ulsen, Paul
TI  - Beth's nonclassical valuations
JO  - Philosophia Scientiae
PY  - 1998-1999
SP  - 279
EP  - 302
VL  - 3
IS  - 4
PB  - Éditions Kimé
UR  - http://www.numdam.org/item/PHSC_1998-1999__3_4_279_0/
LA  - en
ID  - PHSC_1998-1999__3_4_279_0
ER  - 
%0 Journal Article
%A de Jongh, Dick
%A van Ulsen, Paul
%T Beth's nonclassical valuations
%J Philosophia Scientiae
%D 1998-1999
%P 279-302
%V 3
%N 4
%I Éditions Kimé
%U http://www.numdam.org/item/PHSC_1998-1999__3_4_279_0/
%G en
%F PHSC_1998-1999__3_4_279_0
de Jongh, Dick; van Ulsen, Paul. Beth's nonclassical valuations. Philosophia Scientiae, Tome 3 (1998-1999) no. 4, pp. 279-302. http://www.numdam.org/item/PHSC_1998-1999__3_4_279_0/

Beth, Evert W. 1951 A Topological Proof of the Theorem of Löwenheim-Skolem-Gödel, Indagationes Mathematicae, 13, 437-444. | Zbl

Beth, Evert W. 1954a A Subformula Theorem for the Sentential Calculus, and a Characterisation of its Axiom Systems (dedicated to Robert Feys), unpublished.

Beth, Evert W. 1954b A Subformula Theorem for the Sentential Calculus, and a Characterisation of Axiom Systems Adequate for it (dedicated to Robert Feys), rewritten version of 1954a, unpublished.

Beth, Evert W. 1954c A Subformula Theorem for the Sentential Calculus, and a Characterisation of Axiom Systems Adequate for it (abstract for ASL meeting, Amsterdam, September 1, 1954), unpublished.

Beth, Evert W. 1954/ 1955 Nieuwentyt's Significance for the Philosophy of Science, Synthese, 9, 447-453.

Beth, Evert W. 1955a Remarks on Natural Deduction (dedicated to Robert Feys), Indagationes Mathematicae, 17, 322-325. | Zbl

Beth, Evert W. 1955b Semantic Entailment and Formal Derivability, Mededelingen Koninklijke Nederlandse Akademie van Wetenschappen, Nieuwe Reeks, 18, 309-342.

Beth, Evert W. 1955c Poincaré et la philosophie, Le Livre du centenaire de la renaissance de Henri Poincaré, 1854-1954, Paris, 232-238.

Beth, Evert W. 1956a L'Existence en mathématiques, (lectures 1954, March 29-April 2, Paris (Sorbonne)), Paris/Louvain: Gauthiers-Villars/ Nauwelaerts (Collection de logique mathématiques, série A, 10).

Beth, Evert W. 1956b Semantic Construction of Intuitionistic Logic, Mededelingen Koninklijke Nederlandse Akademie van Wetenschappen, Nieuwe Reeks, 19, 357-388. | Zbl

Beth, Evert W. 1957 La crise de la raison et la logique, Paris/Louvain: Gauthiers-Villars/Nauwelaerts, (Collection de logique mathématique, 12, Série A). | Zbl

Beth, Evert W. 1958a Construction sémantique de la logique intuinioniste, Le raisonnement en mathématique et en sciences expérimentales (Paris, Sept. 26-Oct. 1, 1955), in Colloques Int. du C.N.R.S., 70, 77-83.

Beth, Evert W. 1958b On Machines which Prove Theorems, Simon Stevin 32, 49-60 (lecture August 6, 1957, IBM research centre Yorktown, NY). And in [Beth 1962], 112-121. | Zbl

Beth, Evert W. 1959 The Foundations of Mathematics, a Study in the Philosophy of Sciences, Amsterdam: North-Holland, in Studies in logic. | Zbl

Beth, Evert W. 1960a Completeness Results for Formal Systems, Proceeding International Congress Mathematicians (Edinburgh, 1958, August 4-21), Cambridge, 281-288. | Zbl

Beth, Evert W. 1960b Observations on an Independence Proof for Peirce's law, (abstract), The Journal of Symbolic logic, 25, 389 (received Oct. 24, 1961, published Oct., 1962 in no. 4 of vol. 25).

Beth, Evert W. 1961a Méthodes de déduction, vue d'ensemble, Compte-rendu des travaux effectués par l'Université d'Amsterdam dans le cadre du contrat Euratom, Rapport CETIS, 26, (Rapport 1), 5-20.

Beth, Evert W. 1961b Remarques sur la théorie des pseudo-valuations, Compte-rendu des travaux effectués par l'Université d'Amsterdam dans le cadre du contrat Euratom, Rapport CETIS, 26 (Rapport 3, 15 Mai 1961), 32-35.

Beth, Evert W. 1961c Construction sémantique de la logique inférentielle, Compte-rendu des travaux effectués par l'Université d'Amsterdam dans le cadre du contrat Euratom, Rapport CETIS, 26 (Rapport 8, 15 Octobre 1961), 172-178.

Beth, Evert W. 1961d Observations Concerning Computation, Deduction and Heuristics, Compte-rendu des travaux effectués par l'Université d'Amsterdam dans le cadre du contrat Euratom, Rapport CETIS, 26 (Rapport 10, 15 Octobre 1961), 106-119. And in Computer Programming and Formal Systems, Amsterdam, (1963), 21-32, Amsterdam: North-Holland (Studies in Logic). | Zbl

Beth, Evert W. 1962 Formal Methods, an Introduction to Symbolic Logic and to the Study of Effective Operations in Arithmetic and Logic, Dordrecht: Reidel. | Zbl

Beth, Evert W. 1965 Semantische Begründung der derivativen Implikationslogik, Archiv für Mathematische Logik und Grundlagenforschung, 7, 23-28, (received Jan. 6, 1962; in No. 7/1-2: vereinigten Beiträge sind von den Verfasser Herrn Prof.dr Arnold Schmidt zu seinem 60. Geburtstag am 11. Juli 1962 gewidmet worden.). | EuDML | Zbl

Beth, Evert W. and Nieland, Johannes J.F. 1965 Semantic Construction of Lewis's Systems S4 and S5, Symposium of the theory of models (J.W. Addison, L. Henkin, A. Tarski eds.), (Proc. 1963 Int. Symposium Berkeley), Amsterdam, 17-24: North-Holland (Studies in Logic). | Zbl

Bull, R. and Segerberg, K. 1984 Basic Modal Logic, Handbook of philosophical logic II, Extensions of classic logic, (Gabbay, D. & Guenther, F. ed.), 1-88. | Zbl

Church, Alonzo 1956 Introduction to Mathematical logic I, Princeton: Princeton University Press. | Zbl

Davis, Martin 1958 Computability and Unsolvability, New York-Toronto: McGraw-Hill (Series in information processing and computers) | Zbl

De Jongh, Dick H.J. 1962a Recherches sur les I-valuations, Compte-rendu des travaux effectués par l'Université d'Amsterdam dans le cadre du contrat Euratom, Rapport CETIS, 26, 172-178 (Rapport 17).

De Jongh, Dick H.J. 1962 Operators in Inferential Sentential Logic (Euratom-rapport No. 25, November 15, 1962), unpublished.

De Jongh, Dick H.J. 1964 Onderzoekingen over de intuitionistische propositielogica [Investigations in the Intuitionistic Propositional calculus] (doctoraalskriptie; master's thesis, University of Amsterdam), unpublished.

De Jongh, Dick H.J. and Chagrova, L.A. 1995 The Decidability of Dependency in Intuitionistic Propositional Logic, The Journal of Symbolic Logic, 60, 498-504. | Zbl

Dummett, Michael A.E. 1977 Elements of Intuitionism, Oxford: Clarendon Press. | Zbl

Dummett, Michael A.E. and Lemmon, E.J. 1958 Modal Logics between S4 and S5, Zeitschrift für mathematische Logik und Grundlagen der Mathematik, 4, 250-264. | Zbl

Dyson, V.H., and Kreisel, Georg 1961 Analysis of Beth's Semantic Construction of Intuitionistic Logic, Technical Report No. 3, Stanford, California: Office of Ordnance Research, Contract No. DA-04-200-ORD-997; Applied mathematics and statistical laboratories, Stanford University.

Friedman, H.M. 1975 Intuitionistic completeness of Heyting's predicate calculus, Notices of the American Mathematical Society, 22, A-648.

Gödel, Kurt 1933 Eine Interpretation des intuitionistischen Aussagenkalküls, Ergebnisse eines mathematischen Kolloquiums, 7, 23-24. | Zbl

Guillaume, Marcel 1958 Rapports entre calculs propositionnels modaux et topologie impliqués par certaines extensions de la méthode des tableaux sémantiques. Système S4 de Lewis, Système de Feys-von Wright, C.R. Acad. des Sci. (Paris) 246, 1140-1142, 2207-2210; and C.R. Acad. des Sci. 247, 1282-1283. | Zbl

Hendriks, Alex 1996 Computations in Propositional logic (dissertation, University of Amsterdam): ILLC Dissertation Series 1996-01. | Zbl

Hilbert, David and Bernays, P. 1933 Grundlagen der Arithmetik I, Berlin: Julius Springer.

Hintikka, K.J.J. 1961 Modality and Quantification, Theoria, 27, 119-128.

Jónnson, B. and Tarski, A. 1951 Boolean Algebras with Operators I, American Journal of mathematics, 891-939. | Zbl

Kamp, Hans and De Jongh, Dick H.J. 1964 LISP-ALGOL-programma voor de intuitionistische propositielogica, [LISP-ALGOL program for the intuitionistic propositional calculus] (R 1014, codenr. JON 260364/7266 and R 1057 codenr. JON 260364/8615), typescript, unpublished.

Kanger, Stig 1957 Provability in Logic, Stockholm: Almqvist and Wiksell. | Zbl

Kreisel, Georg Review of [Beth 1956b], Zentralblatt für Mathematik, 73, 249-250.

Kripke, Saul A. 1959a A Completeness Theorem in Modal Logic, The Journal of Symbolic Logic, 24, 1-14 (received August 25, 1958, published Nov. 26, 1959, in no. 1 of vol. 24). | Zbl

Kripke, Saul A. 1959b Semantical Analysis of Modal Logic, (abstract), The Journal of Symbolic Logic, 24, 323-324 (received Oct. 21, 1959, published March 24, 1961, in no. 4 of vol. 24). | Zbl

Kripke, Saul A. 1963a Semantical Analysis of Modal Logic I, Normal Modal propositional calculi, Zeitschrift für math. Logik und Grundlagen der Math., 9, 67-96. | Zbl

Kripke, Saul A. 1963b Semantical Considerations on Modal Logic, Acta Philosophica Fennica, 16, 83-94. | Zbl

Kripke, Saul A. Semantic Analysis of Intuitionistic Logic I, Formal Systems and Recursive Functions (Proc. Eight Logic Colloquium, Oxford, July 1963), Amsterdam: North-Holland (Studies in Logic 125), 92-130. | Zbl

Lineal, S.L. and Post, Emil L. 1949 Recursive Unsolvability of the Deducibility, Tarski's Completeness, and the Independence of Axioms Problems of Propositional calculus, Bulletin of the American Mathematical Society, 55 (abstract 39), p. 50.

Mckinsey, J.C.C. 1945 On the Syntactical Construction of Systems of Modal Logic, The Journal of Symbolic Logic, 10, 83-94. | Zbl

Mckinsey, J.C.C. and Tarski, A. 1948 Some Theorems about the Sentential Calculi of Lewis and Heyting, The Journal of Symbolic Logic, 13, 1-15. | Zbl

Maehara, S. 1954 Eine Darstellung der intuitionistischen Logik in der klassischen, Nagoya Mathematical Journal, 7, 45-64. | Zbl

Nieland, Johannes J.F. 1960 Nieuwe onderwerpen te verzorgen door J.J.F. Nieland, bijeenkomst over Kripke op 4, 16, 18 Mei, 1960 in E.W. Beth, privatissimum, Logica en Wijsbegeerte der Exacte Wetenschappen, no. 158-160.

Nieland, Johannes J.F. and Beth, Evert W. 1961 Construction sémantique du système S4. Compte-rendu des travaux effectués par l'Université d'Amsterdam dans le cadre du contrat Euratom, Rapport CETIS, 26 (Rapport no. 6), 66-74.

Notulenboek 1961/ 1963 Notulenboek [Minutes] Euratom, unpublished.

Tarski, Alfred 1947 Problems of Mathematics, Princeton University Bicentennial Conferences 1946, Series 2, Conference 2, 10-12: Princeton University Press. | Zbl

Troelstra, Anne S. 1977 Choice Sequences, a Chapter of Intuitionistic Mathematics, Oxford: Clarendon Press. | MR | Zbl

Troelstra, A.S. and Schwichtenberg, H. 1996 Basic Proof Theory, Cambridge: Cambridge University Press. | MR | Zbl

Veldman, W. 1976 An Introduction to the Intuitionistic Completeness Theorem for Intuitionistic Predicate Logic, The Journal of Symbolic Logic, 41, 159-166. | MR | Zbl

Yntema, Mary K. 1964 A Detailed Argument for the Post-Lineal Theorems, Notre Dame Journal of formal Logic, 5 (No. 1), 37-50. | MR | Zbl