Bulletin of the American Mathematical Society

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Book Information:

Author: A. G. Dragalin
Title: Mathematical intuitionism. Introduction to proof theory
Additional book information: Translations of Mathematical Monographs, Vol. 67. Translated by E. Mendelson. American Mathematical Society, Providence, R. I., 1988, ix+228 pp., $75.00. ISBN 0-8218-4520-9.

E. W. Beth, Semantic construction of intuitionistic logic, Nieuwe Reeks, Deel 19, No. 11, N. V. Noord-Hollandsche Uitgevers Maatschappij, Amsterdam, 1956. Medededlingen der koninklijke Nederlandse Akademie van Wetenschappen, afd. Letterkunde. MR 0089152

Paul J. Cohen, Set theory and the continuum hypothesis, W. A. Benjamin, Inc., New York-Amsterdam, 1966. MR 0232676

Eduardo J. Dubuc, $C^{\infty }$-schemes, Amer. J. Math. 103 (1981), no. 4, 683–690. MR 623133, DOI 10.2307/2374046

M. P. Fourman and D. S. Scott, Sheaves and logic, Applications of sheaves (Proc. Res. Sympos. Appl. Sheaf Theory to Logic, Algebra and Anal., Univ. Durham, Durham, 1977) Lecture Notes in Math., vol. 753, Springer, Berlin, 1979, pp. 302–401. MR 555551

Théorie des topos et cohomologie étale des schémas. Tome 2, Lecture Notes in Mathematics, Vol. 270, Springer-Verlag, Berlin-New York, 1972 (French). Séminaire de Géométrie Algébrique du Bois-Marie 1963–1964 (SGA 4); Dirigé par M. Artin, A. Grothendieck et J. L. Verdier. Avec la collaboration de N. Bourbaki, P. Deligne et B. Saint-Donat. MR 0354653

J. M. E. Hyland, The effective topos, The L.E.J. Brouwer Centenary Symposium (Noordwijkerhout, 1981) Studies in Logic and the Foundations of Mathematics, vol. 110, North-Holland, Amsterdam-New York, 1982, pp. 165–216. MR 717245

S. C. Kleene, On the interpretation of intuitionistic number theory, J. Symbolic Logic 10 (1945), 109–124. MR 15346, DOI 10.2307/2269016

Anders Kock, Synthetic differential geometry, London Mathematical Society Lecture Note Series, vol. 51, Cambridge University Press, Cambridge-New York, 1981. MR 649622

Saul A. Kripke, Semantical analysis of intuitionistic logic. I, Formal Systems and Recursive Functions (Proc. Eighth Logic Colloq., Oxford, 1963) North-Holland, Amsterdam, 1965, pp. 92–130. MR 0201300

R. Lavendhomme, Leçons de géométrie différentielle synthétique naïve, Monographies de Mathématique [Mathematical Monographs], vol. 3, Université Catholique de Louvain, Institut de Mathématique Pure et Appliquée, Louvain-la-Neuve; Centrale d’Achats et Service d’Impression (CIACO), Louvain-la-Neuve, 1987 (French). MR 933087

Ieke Moerdijk and Gonzalo E. Reyes, A smooth version of the Zariski topos, Adv. in Math. 65 (1987), no. 3, 229–253. MR 904724, DOI 10.1016/0001-8708(87)90023-5

Abraham Robinson, Non-standard analysis, North-Holland Publishing Co., Amsterdam, 1966. MR 0205854

Myles Tierney, Sheaf theory and the continuum hypothesis, Toposes, algebraic geometry and logic (Conf., Dalhousie Univ., Halifax, N.S., 1971) Lecture Notes in Math., Vol. 274, Springer, Berlin, 1972, pp. 13–42. MR 0373888

A. S. Troelstra and D. van Dalen, Constructivism in mathematics. Vol. I, Studies in Logic and the Foundations of Mathematics, vol. 121, North-Holland Publishing Co., Amsterdam, 1988. An introduction. MR 966421

1.

E. W. Beth, Semantic construction of intuitionistic logic, Kon. Ned. Ak. Wet. 19 (1956), 357-388. MR 0089152

2.

P. J. Cohen, Set theory and the continuum hypothesis, Benjamin, New York, 1966. MR 232676

3.

E. Dubuc, C, Amer. J. Math 103 (1981). MR 623133

4.

M. Fourman and D. Scott, Sheaves and logic, in Application of Sheaves, Springer LNM 753, 1979, pp. 280-401. MR 555551

5.

A. Grothendieck, et al., Theorie des topos et cohomologie étale des schémes, Springer LNM 269, 1972. MR 354653

6.

J. M. E. Hyland, The effective topos, The L. E. J. Brouwer Centenary Sympos. (A. S. Troelstra, D. van Dalen, eds.), North-Holland, Amsterdam, 1982. MR 717245

7.

S. C. Kleene, On the interpretation of intuitionistic number theory, J. Symbolic Logic 10 (1945), 109-124. MR 15346

8.

A. Kock, Synthetic differential geometry, Cambridge Univ. Press, Cambridge, United Kingdom, 1981. MR 649622

9.

S. Kripke, Semantical analysis of intuitionistic logic, I, in Formal Systems and Recursive Functions (J. Crossely and M. A. E. Dummett, eds.), North-Holland, Amsterdam, 1965, pp. 92-130. MR 201300

10.

R. Lavendhomme, Leçons de géométrie différentielle synthétique naïve, CIACO, Louvain-la-Neuve, 1987. MR 933087

11.

I. Moerdijk and G. E. Reyes, A smooth version of the Zariski topos, Adv. Math. 65 (1987), 229-253. MR 904724

12.

A. Robinson, Non-standard analysis, North-Holland, Amsterdam, 1966. MR 205854

13.

M. Tierney, Sheaf theory and the continuum hypothesis, in Toposes, Algebraic Geometry and Logic (F. W. Lawvere, ed.), Springer LNM 274, 1972. MR 373888

14.

A. S. Troelstra and D. van Dalen, Constructivism in mathematics, vol. II, North-Holland, Amsterdam, 1988. MR 970277