BIBLIOGRAPHY OF A.S. TROELSTRA

Books (Mathematics)

1969A     Principles of intuitionism. Lectures presented at theSummer Conference on Intuitionism and Proof  Theory (1968) at SUNYat Buffalo, N.Y.}, Springer-Verlag,   Berlin.111 pages.

1973       (with C.A. Smorynski, J.I. Zucker, W.A.Howard) Metamathematical Investigationof intuitionistic Arithmetic and
Analysis , Springer Verlag, Berlin, 1--323. Chapters I--IV were written by A.S. Troelstra. A 2nd corrected edition appeared  in 1993, as a report: ILLC Prepublication Series X-93-05, Universiteit van Amsterdam.

1977D      Choice Sequences, a Chapter of Intuitionistic Mathematics, Clarendon Press, Oxford. 170 pages.

1988        (with D. van Dalen) Constructivismin Mathematics. An Introduction, Amsterdam, North-Holland Publ. Co. Vol.1: xx + 342 + XIV pages; Vol. 2: xviii + pages 345--880 + LII pages.

1992        Lectures on Linear Logic, CSLI Stanford, Lecture Notes Series nr. 29.

1996A     (with H. Schwichtenberg) Basic ProofTheory , Cambridge University Press, Cambridge U.K.
Second, revised and expanded edition 2000.

Papers (Mathematics)

1965        Over een stelling van P. Zeeman en een stelling uit de affiene meetkunde (Dutch), Nieuw Tijdschrift voor Wiskunde52, 132--136.

1965A      On intermediate propositional logics, Indagationes Mathematicae 27, 141--152.

1966         Intuitionistic general topology, Ph. D.thesis, University of Amsterdam. 112 pages.

1966A      (with D.H.J. de Jongh) On the connection of partially ordered sets with some pseudo-boolean algebras, Indagationes Mathematicae 28, 317--329.

1967         Intuitionistic continuity, Nieuw Archief voor Wiskunde, 3rd series 15, 2--6.

1967A     Finite and infinite in intuitionistic mathematics, Compositio Mathematica 18, 94--116.

1967B     Intuitionistic connectedness, Indagationes Mathematicae 29, 96--105.

1968     The theory of choice sequences, in: B. van Rootselaar, J.F.Staal (eds), Logic, Methodology and Philosophy of Science III, North-Holland Publ. Co., Amsterdam, 289--298.

1968A     The use of "Brouwer's principle" in intuitionistic topology, in : H.A.Schmidt, K. Schütte, H.-J. Thiele (eds), Contributions to mathematicallogic. Proceedings of the Logic Colloquium, Hannover, 1966 , North-HollandPubl. Co., Amsterdam, 289--298.

1968B     The scientific work of A. Heyting, Compositio Mathematica 20, 3--12.

1968C     New sets of postulates for intuitionistic topology, Compositio Mathematica 20, 211--221.

1968D     One-point compactifications of intuitionistic locally compact spaces, Fundamenta Mathematicae 62, 75--93.

1969     Informal theory of choice sequences (with summaries in Russian and Polish), Studia Logica 25, 31--52.

1969B     Notes on the intuitionistic theory of sequences (I), Indagationes Mathematicae 31, 430--440.

1970     (with G. Kreisel) Formal systems for some branches ofintuitionistic analysis, Annals of Mathematical Logic 1, 229--387.

1970A     (with D. van Dalen) Projections of lawless sequences, in: J. Myhill, A. Kino, R.E.Vesley (eds), Intuitionism and Proof theory , North-Holland Publ. Co., Amsterdam, 163--186.

1970B     Notes on the intuitionistic theory of sequences (II), Indagationes Mathematicae 32, 99--109.

1970C     Notes on the intuitionistic theory of sequences (III), Indagationes Mathematicae 32, 245--252.

1971     Notions of realizability for intuitionistic arithmetic and intuitionistic arithmetic in all finite types, in: J.E. Fenstad (editor), Proceedings of the second Scandinavian Logic Symposium, North-Holland Publ. Co., Amsterdam, 369--425.

1971A     An addendum, Annals of Mathematical Logic 3, 437--439.

1971B    Intuitionisme (Dutch), Wijsgerig perspectief op Wetenschap en Maatschappij 11, 255--267.

1971D    Computability of terms and notions of realizability for intuitionistic analysis. Report 71--02, Department of Mathematics, University of Amsterdam. 60 pages.

1973A    Notes on intuitionistic second-order arithmetic, in:A. R. D. Mathias, H. Rogers (eds), Cambridge Summer School in Mathematical Logic , Springer Verlag, Berlin, 171--205.

1974A    Note on the fan theorem, The Journal of Symbolic Logi c 39, 584--596.

1974B    Corrections and additions to ``Metamathematical Investigation of intuitionistic Arithmetic and Analysis''. Report 74--16, Department of Mathematics, University of Amsterdam. 26 pages.

1975    Non-extensional equality, Fundamentae Mathematicae 82, 307--322.

1975A    Markov's principle and Markov's rule for theoriesofchoice sequences, in: J. Diller, G. H. Müller (eds), Proof TheorySymposiumKiel 1974 , Springer Verlag, Berlin, 370--383.

1977    Some models for intuitionistic finite-type arithmeticwith fan functional, The Journal of Symbolic Logic 42, 194--202.

1977A    Axioms for intuitionistic mathematics incompatible with classical logic, in: R. Butts, J. Hintikka (eds), Logic, Foundations of Mathematics and Computability Theory (Part One of the Proceedings of theFifth International Congress on Logic, Methodology and Philosophy of Science; London, Ontario, Canada 1975), Reidel, Dordrecht, 59--84.

1977B    Completeness and validity for intuitionistic predicate logic, in: M. Guillaume (editor), Colloque international de Logique, Clermont--Ferrand 18--25 juillet 1975, Éditions du C.N.R.S, Paris (Colloques internationaux du Centre National de la Récherche Scientifique nr. 249) 39--58.

1977C    Special instances of generalized continuity which are conservative over intuitionistic arithmetic, Indagationes Mathematicae 39, 55--65.

1977E    A note on non-extensional operations in connection with continuity and recursiveness, Indagationes Mathematicae 39, 455--462.

1977F    Aspects of constructive mathematics, in: K.J.Barwise(editor), , North-Holland Publ. Co., Amsterdam,973--1052.

1978    Appendix to D. van Dalen's ``An interpretation of intuitionistic analysis'', Annals of Mathematical Logic 13, 40--41.

1978A    A. Heyting on the formalization of intuitionistic mathematics. Commentary by A. S. Troelstra, in: E. M. J. Bertin, H. J. M. Bos, A. W. Grootendorst (eds), Two decades of Mathematics in the Netherlands 1920--1940. A Retrospection on the Occasion of the Bicentennial of the Wiskundig Genootschap, Mathematisch Centrum, Amsterdam, Part I, 153--175.

1978B    Some remarks on the complexity of Henkin-Kripke models, Indagationes Mathematicae 40, 296--302.

1979    A supplement to "Choice Sequences". Report 79--04, Department of Mathematics, University of Amsterdam.

1979A    On Ashvinikumar's principle of microscopic completeness, Indagationes Mathematicae 41, 77--81.

1979B    (with G. F. van der Hoeven) Projections of lawless sequences II, in: M. Boffa, D. van Dalen and K. McAloon (eds), Logic Colloquium7 8 , North-Holland Publ. Co., Amsterdam, 265--298.

1980    Extended bar-induction of type 0, in: J. Barwise, H. J. Keisler and K. Kunen (eds), The Kleene Symposium , North-Holland Publ. Co., Amsterdam, 277--316.

1980A    The interplay between logic and mathematics: intuitionism, in: E. Agazzi (editor), Modern Logic: A Survey , Reidel, Dordrecht, 197--221.

1980B    Intuitionistic extensions of the reals, Nieuw Archief voor Wiskunde (3) 28, 63--113.

1981    Arend Heyting and his contribution to intuitionism, Nieuw Archief voor Wiskunde (3) 29, 1--23.

1981A    (with J. Niekus, H. van Riemsdijk) Bibliography of A. Heyting, Nieuw Archief voor Wiskunde (3) 29, 24--35.

1981B    Levensbericht van Arend Heyting (9 mei 1898 - 9 juli1980), in: Jaarboek van de Koninklijke Nederlandse Akademie van Wetenschappen 1980, North-Holland Publ. Co., Amsterdam, 172--175 (with photograph).

1981C    On a second-order propositional operator in intuitionistic logic, Studia Logica 40, 113--139.

1981D    Lawless sequences and their uses, in: S. Bernini (editor), Atti del Congresso Nazionale di Logica. Montecatini Terme 1-5 Ottobre1979 , Bibliopolis, Naples, 165--173.

1981E    Naschrift (Dutch), Nieuw Archief voor Wiskunde (3) 29, 134--135. (Postscript to: A. Heyting, Continuum en Keuzerij bij Brouwer, 125-139.)

1982    On the origin and development of Brouwer's concept ofchoice sequence, in: A. S. Troelstra, D. van Dalen (eds), The L. E. J.Brouwer Centenary Symposium, North-Holland Publ.Co., Amsterdam, 465--486.

1982B    Intuitionistic extensions of the reals II, in : D. van Dalen, D. Lascar, J. Smiley (eds), Logic Colloquium '80, North-Holland Publ.Co., Amsterdam, 279--310.

1983    Logic in the writings of Brouwer and Heyting, in: V. M. Abrusci, E. Casari, M. Mugnai (eds), Atti del Convegne Internazionaledi Storia della Logica. San Gimignano, 4--8 dicembre 1982, CLUEB, Bologna, 193--210.

1983A    Analyzing choice sequences, Journal of Philosophical Logic 12, 197--260.

1983B    Definability of finite sum types in Martin-Löf's type theories, Indagationes Mathematicae 45, 475--481.

1984    (with J.Diller) Realizability and intuitionistic logic, Synthese 60, 253--282.

1985    Choice sequences and informal rigour, Synthese62, 217--227.

1986    Introductory note to 1932, in: K. Goedel, Collected Works, Volume I (S. Feferman et al., editors), Oxford University Press, Oxford, 222--223.

1986A    Introductory note to 1933e, in: K. Goedel, Collected Works, Volume I (S. Feferman et al., editors), Oxford University Press, Oxford, 282--287.

1986B    Introductory note to 1933f, in: K. Goedel, Collected Works, Volume I (S. Feferman et al., editors), Oxford University Press, Oxford, 296--299.

1986C    Strong normalization for typed terms with surjectivepairing, Notre Dame Journal of Formal Logic 27, 547--550.

1987       On the syntax of Martin-Lof's type theories, TheoreticalComputer Science 51, 1--26.

1988A    A short course in intuitionistic metamathematics,in: A. Zanardo (editor), Atti degli Incontri di Logica Matematica, Vol.\4. XI Incontro: Siena, 27--30 maggio 1987. Fondamenti della Matematica .Scuola di Specializzione in Logica Matematica, Dipartimento di matematica,Università di Siena, 9--14.

1988B    Validity and completeness for intuitionistic predicate logic, in: A. Zanardo (editor), Atti degli Incontri di Logica Matematica. Vol. 4. XI Incontro: Siena, 27--30 maggio 1987. Fondamenti della Matematica , Scuola di Specializzione in Logica Matematica, Dipartimento di matematica, Università di Siena, 15--21.

1989    Index of the Heyting Nachlass, University of Amsterdam, ITLI Prepublication Series X--89--03, 44 pages.

1989A    Article ``Arend Heijting'' (Dutch) in: J.Charité (editor),Biografisch Woordenboek van Nederland III , Instituut voor NederlandseGeschiedenis, 's Gravenhage, 254--256.

1990    Introductory Note to 1958, 1972, in: K. G\"odel, Collected Works II (S. Feferman et al. editors), Oxford University Press, New York, 217--256.

1990A    Remarks on intuitionism and the philosophy of Mathematics, in: G. Corsi, G. Sambin (eds), Atti del Congresso ``Nuovi Problemi della Logica e della Filosofia della Scienza", Viareggio, 8--13 gennaio 1990, Volume II -- Logica , CLUEB, Bologna, 211--228.

1990B    On the early history of intuitionistic logic, in: P.P. Petkov (editor), Mathematical Logic, Plenum Press, New York andLondon, 3--17.

1991    History of Constructivism in the Twentieth Century, University of Amsterdam, ITLI Prepublication Series ML-91-05.

1992A    Comparing the theory of representations and constructive mathematics, in: E. Börger, G. Jäger, H. Kleine-Büning, M. M. Richter(eds), Computer Science Logic, 5th workshop, CSL'91, Springer Verlag, Berlin, 382--395

1993    Metamathematical Investigation of Intuitionistic Arithmetic and Analysis. Corrections to the first edition. ILLC Prepublication Series X-93-04, Universiteit van Amsterdam.

1994    Tutorial on Linear Logic, in: K. Dosen, P. Schroeder-Heister, Substructural Logics , Clarendon Press, Oxford, 327--355.

1995    Introductory note to *1941, in: K. Gödel,CollectedWorks III , Oxford University Press, Oxford, 186--189.

1995A    Natural deduction for intuitionistic linear logic, Annals of Pure and Applied Logic 73, 79--108.

1995B  Structurele Bewijstheorie. Verslagen van de gewone vergaderingen der Afdeling Natuurkunde der KNAW, 113--117.

1996     Choice sequences: a retrospect, CWI Quarterly 9 (1--2), 143--149.

1998    Concepts and Axioms. Philosophia Mathematica, series III 6, 195--208.

1998A    Realizability, in: S. Buss (editor), Handbook of Proof Theory , Elsevier, Amsterdam, 407--473. Preprint: ILLC prepublication series ML-92-09, Universiteit van Amsterdam 1992.

1999    From Constructivism to Computer Science, Theoretical Computer Science 211, 233--252. Text of the lecture held on occasion of receiving the F.L. Bauer-prize. Preprint: ILLC Research report CT-96-02.

1999A    Marginalia on sequent calculi, Studia Logica 62, 291--303. Preprint: ILLC Research report ML-1998-01, University of Amsterdam.

1999B    (with S. Artemov, B. Kushner, G. Mints, E. Nogina) In Memoriam: Albert Dragalin, 1941--1998, The Bulletin of Symbolic Logic   5, 389--391.

2001      Honderd jaar keuzenrijen. Verslagen van de gewone vergaderingen der Afdeling Natuurkunde der KNAW, 223--227

Non-mathematical publications

1995      Over geloof en natuurwetenschap. In: A. v.d. Beek (editor), Lichtgeraakt. Wetenschapsbeoefenaren over de relatie van hun Christen-zijn en hun 
werk. Callenbach, Nijkerk, 26--35. (Dutch)

2005 Historische inleiding, in: H.A. Lorentz , Zwarte mensen, witte bergen. Uitgeverij Atlas, Amsterdam/Antwerpen (Dutch).

2003      Tijgers op de Ararat. Natuurhistorische Reisverhalen 1700--1950. Uitgeverij Atlas, Amsterdam/Antwerpen. 605 pp. (Dutch)

2007 Van Spitsbergen tot Suriname. Nederlandse biologen, geologen en natuurliefhebbers op reis. Bloemlezing, met algemene inleiding en inleidingen bij elke schrijver.

Uitgeverij Atlas, Amsterdam/Antwerpen.

2009 Kolibries in de oren. Uitgeverij Atlas, Amsterdam/Antwerpen.