Prof. Erwin Engeler

• Dates and Stations
• Activities and Offices
• Publications
  1. Classical model theory and infinitary languages
  2. Categories in model theory
  3. Algorithmic properties of structures and logics of programs
  4. Galois connections and structure of programs
  5. Foundations and philosophy of science
  6. Combinatory algebra as a foundational structure for mathematics
  7. Neuroscience
  8. Miscellaneous
• Current Projects and Talks

Dates and Stations

1955

Diploma in mathematics at the ETH, Zurich

1956

Marriage to Margaret née Knecht, Dr.phil. (Two children, Christopher, Dr.med. and Suzanne, Dr.iur.)

1958

Dr.sc.math. ETH, Zurich (Prof. P. Bernays)

1958

Assistant Professor at the University of Minnesota

1962/63

Assistant Professor at the University of California, Berkeley

1964/72

Associate Professor and Full Professor at the University of Minnesota

1972/97

Professor of Logic and Computer Science, Mathematics Department, ETH, Zurich

Activities and Offices

• Author of various books on Logic, Mathematics and Computer Science, translated into Russian, Japanese and Chinese
• Editor of scientific journals, book series and symposia
• Collected works 1993
• Active interest in music, art and various outdoor sports, mineralogy
• Member of
  • Academia Europaea
  • ACM (Association for Computing Machinery), named Fellow 1997
  • The American Mathematical Society
  • The Swiss Mathematical Society
  • The Swiss National Research Council (1985 - 1997)
  • The Swiss Association for the Promotion of Computer Science and its Applications (as President 1987 - 1997), now SARIT
  • numerous other societies
• Students see Genealogy Project of the AMS

Publications

1. Classical model theory and infinitary languages
   
   
   • Untersuchungen zur Modelltheorie. Diss. ETH (1958).
   • Aequivalenzklassen von n -Tupeln. Z. Math. Logik Grundl. Math. 5 (1959) 340-345.
   • Eine Konstruktion von Modellerweiterungen. Z. Math. Logik Grundl. Math. 5 (1959) 126-131.
   • Unendliche Formeln in der Modelltheorie. Z. Math. Logik Grundl. Math. 7 (1961) 154-160.
   • Zur Beweistheorie von Sprachen mit unendlich langen Formeln. Z. Math. Logik Grundl. Math. 7 (1961) 213-218.
   • A reduction principle for infinite formulas. Mathem. Annalen 151 (1963) 296-303.
   
   
2. Categories in model theory
   
   
   • Models with prescribed second-order properties. J. Symbolic Logic 37 (1962) 476.
   • Combinatorial theorems for the construction of models. In: The Theory of Models. Proc. 1963 Int. Symp., eds J.W. Addison et al. (North-Holland: Amsterdam, l965) pp. 77-88.
   • Categories of mapping filters. In: Conf. Categorical Algebra, eds S. Eilenberg et al. (Springer: New York, 1966) pp. 247-253. (PDF)
   • On structures defined by mapping filters. Math. Annalen 167 (1966) 105-112.
   • On the structure of elementary maps. Z. Math. Logik u. Grundl. d. Math. 13 (1967) 323-328.
   • (with H. Röhrl) On the problem of foundations of category theory. Dialectica 23 (1969) 58-66.
   
   
3. Algorithmic properties of structures and logics of programs
   
   
   • Algorithmic properties of structures. Math. Systems Theory 1 (1967) 183-195.
   • Formal Languages: Automata and Structures. (Markham: Chicago 1968) 81 pp.
   • Remarks on the theory of geometrical constructions. In: Syntax & Semantics of Inf. Lang., ed. J. Barwise, Springer Lecture Notes in Mathematics 72, (Springer: New York, 1968) 64-76. (PDF)
   • Proof theory and the accuracy of computations. In: Symp. Automatic Demonstr., eds M. Laudet et al.), Springer Lecture Notes in Mathematics 125 (Springer: New York 1970) 62-72.
   • Algorithmic approximations. J. Comp. Systems Sci. 5 (1971) 67-82
   • (ed) Symposium on Semantics of Algor. Languages, Springer Lecture Notes in Mathematics 188 (Springer: New York, 1971)
   • Structure and meaning of elementary programs. ibid. 89-101.
   • Introduction to the theory of computation. (Academic Press: New York, 1973), 231 pp. (Transl. into Japanese 1975).
   • The logic of "can do", Logic of Programming. In: Int. Symp. on Theoretical Computer Science eds A. Ershov et al., Springer Lecture Notes in Computer Science 5, (1974) 17-28.
   • Algorithmic logic. Math. Center Tracts 63 (1975) 57-85.
   • (ed) Logic of Programs. Springer Lecture Notes in Computer Science 125 (Springer: New York, 1981).
   • Logic in Computer Science. In: Information Processing 86 ed. H.J. Kugler (North-Holland, Amsterdam, 1986), 393.
   
   
4. Galois connections and structure of programs
   
   
   • On the structure of algorithmic problems. GI Fachtagung über Automatentheorie und formale Sprachen. Springer Lecture Notes in Computer Science 2 (Springer: New York, 1973) 2-15.
   • Towards a Galois theory of algorithmic problems. Math. Found. of Comp. Sc. (eds J. Becvar et al.), Slovac Academy of Science: 1973) 51-55.
   • On the solvability of algorithmic problems. Logic Colloquium 73 eds H.E. Rose et al. (North-Holland, Amsterdam, 1975) 231-251. (PDF)
   • Lower bounds by Galois theory. Asterisque 38 (1976) 45-52.
   • Structural relations between programs and problems. Int. Congr. Logic Math. & Phil. Sci. London Ont 1975, Logic, Found. of Math. and Computability, eds Butts et al., (Reidel: Dordrecht, 1977) 267-280.
   • Generalized Galois theory and its application to complexity. Theoret. Comput. Sci. 13 (1981) 271-293. (PDF)
   
   
5. Foundations and philosophy of science
   
   
   • Geometry and language. Dialectica 24 (1970) 77-85.
   • Metamathematik der Elementarmathematik (Springer: New York, 1983) 132 pp.
   • English Translation: Foundations of Mathematics (Springer, 1993) 100 pp.
   • (Transl. into Russian 1987, Transl. into Chinese 1995).
   • Zum logischen Werk von Paul Bernays. Dialectica 32 (1978) 191-200.
   • An algorithmic model of strict finitism. Colloq. Math. J. Bolyai (1978) 345-357. (PDF)
   • Die Skepsis der Mathematiker gegenüber der Grundlagenrhetorik. In: Wozu Wissenschaftsphilosophie? eds P. Hoyningen-Huene et al. (de Gruyter, 1988) 310-313.
   • Zur wissenschaftstheoretischen Bedeutung der kombinatorischen Algebra. In: Jahrbuch der Kurt Goedel Gesellschaft, (Wien 1990) pp. 45-53.
   • The technical problem of "full abstractness" as a model for an issue in reductionism. In: The Problem of Reductionism in Science ed. E. Agazzi (Kluwer, 1991) 91-99.
   • Existenz und Negation. In: Jahrbuch der Kurt Goedel Gesellschaft, (Wien 1994), pp. 37-53. (PDF)
   • Formal Universes. In: Logic Rewriting and Concurrency, N.Marti-Oliet et al., eds. Springer Lecture Notes in Computer Science, vol.9200. 255-263 (2015) (PDF)
   • A Forgotten Theory of Proofs? In: Logical Methods in Computer Science, Volume 15:3 (2019), 7:1-7:6. (PDF)
   
   
6. Combinatory algebra as a foundational structure for mathematics
   
   
   • A new type of models of computation. Math. Found. Comp. Sci. ed J. Gruska, Springer Lecture Notes in Computer Science 53 (Springer: New York, 1977) 52-58.
   • Formal models of computation in which data are processes: theory and applications. Int. Conf. Math. Stud. Info. Proc. Kyoto (1978) 541-558.
   • Algebras and combinators. Algebra Universals 13 (1981) 389-392. (PDF)
   • Equations in combinatory algebras. In: Logics of Programs eds E. Clarke et al., Springer Lecture Notes in Computer Science 164 (Springer: New York, 1984) 193-205. (PDF)
   • Modelling of cooperative processes. In: Comput. Theory and Logic ed. E. Böger. Springer Lecture Notes in Computer Science 270 (Springer: New York, 1987) 143-153.
   • Cumulative type logic programs and modelling. J. of Symbolic Logic 52 (1987) 1059.
   • Cumulative logic programs and modelling. In: Logic Colloquium 1986 eds F.R. Drake et al. (North-Holland, Amsterdam, 1988) 83-93. (PDF)
   • Modelling interacting intelligent systems in the legal context. Neue Methoden im Recht 5 (Attempto Verlag Tübingen 1989), pp. 73-79.
   • Representation of varieties in combinatory algebras. Algebra Universalis 25 (1988) 85-95.
   • Sketch of a new discipline of modelling. Computer Mathematics. Proc. 0f the Special Program at Nankai Institute of Mathematics (1991) 66-76.
   • Combinatory differential fields. Theoretical Computer Science 72 (1990) 119-131. (PDF)
   • Algorithmic Properties of Structures Selected papers of E. Engeler. World Publ. Co., 1994
   • The Combinatory Programme (with K. Aberer et al.) Birkhäuser Boston, 1995, 143 pp. (View the introduction in PDF format.)
   • Computing Aspects of Set Theory (Postscript, PDF). In: Logic and Software Engineering, eds. A. Pnueli and H. Lin (World Scientific, Singapore 1996) pp. 122-126.
   
   
7. Neuroscience
   
   
   • The Neural Net of the Tapeworm Turingia universalis Wolfram. (Manuscript 2007) (PDF)
   • Neural Algebra and Consciousness. K. Horimoto et al. (Eds.): Algebraic Biology 2008, LNCS 5147, pp. 96-109, 2008. © Springer-Verlag Berlin Heidelberg 2008. (PDF)
   • Algebras of the Mind and Algebras of the Brain, Abstracts, 14th Congress of Logic, Methodology and Philosophy of Science, Nancy (France), 2011, p. 204. (PDF)
   • Neural Algebra and Modeling, Abstract of invited talk, AMS-ASL Joint Meeting, Seattle Jan. 2016 (PDF); Manuscript, Feb. 2016 (PDF)
   • Neural Algebra on "How does the Brain Think?", Theoretical Computer Science 777 (2019), 296-307. (PDF)
   
   
8. Miscellaneous
   
   
   • Analogie-Rechengerät ARZ. Anleitung. (Guettinger: Niederteufen, 1956) 20 pp.
   • Über die Monte-Carlo Methode. Mitt. Schweiz. Vers.-math. 58 (1958) 67-76.
   • Lineares Programmieren. Mitteilungsblatt Nr. 4 (Guettinger: Niederteufen, 1958) 10 pp.
   • Über elektr. Analogierechenanlagen für chem. & biol. Vorgänge. Jahrbuch Chem. Industrie 1958/59, 92-95.
   • (With A.P. Speiser) Zur Analogie zwischen einer elektronischen Rechenmaschine und dem Gehirn. Vierteljahresschr. d. Natf. Gesellsch. in Zürich 109 (1964) 81-84.
   • (With R. Maeder) Scientific Computation: The integration of symbolic, numeric and graphic computation. In: Eurocal '85 ed. B. Buchberger, Springer Lecture Notes in Computer Science 203 (Springer: New York, 1985) 185-200.
   • Goals and design considerations for a mathematical laboratory. SIGSAM Bulletin 21 (1987) 7-8.
   • Berechnungstheorie für Informatiker (with P. Lächli, R. Peikert), Teubner, Stuttgart (1988)
   • Grenzen - des Computers? (Introduction to) Grenzen des Computers ed. C. Schnell (Sauer 1991).
   • Wie die Mathematik zum Computer kam (PDF). Abschiedsvorlesung ETH Zürich, 10. Dez. 1996.
   • Forschungspolitik und akademische Privatinitiative. Festschrift Urs Hochstrasser, 1996, pp. 56-60. (HTML)
   • In Memoriam: Ernst Specker 1920-2011. The Bulletin of Symbolic Logic, 18 (2012), 413-417. (PDF)
   • Bernays Lectures 2012. Eröffnungsansprache (Manuscript 2012). (PDF)
   • Remembering Ernst Specker (1920-2011). Elemente Math. 67 (2012), 1-27. (With N. Hungerbühler and J. Makowski) (PDF)
   • Meine persönliche Beziehung zu Konrad Zuse. In: Bruderer 2013, ETH Research Collection (PDF)

Current Projects and Talks

• Thoughts on the Brain, Manuscript, November 2014. (PDF)
• A General Approach to Bürgi's artificium, Manuscript, June 2016 (PDF)
• Neural Algebra. A model of interacting brain functions. Manuscript, Dec. 2016 (PDF)



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