Skip to main content

Leon Henkin

  • Chapter
  • 722 Accesses

Part of the book series: Studies in Universal Logic ((SUL))

Abstract

Leon Henkin was born in 1921 in Brooklyn, New York, in the heart of a Jewish family that originally came from Russia. He died at the beginning of November in 2006. He was an extraordinary logician, an excellent teacher, a dedicated professor, and an exceptional person overall. He had a huge heart and he was passionately devoted to his ideas of pacifism and socialism (in the sense of belonging to the left). He not only believed in equality, but also worked actively to see that it was brought about.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    In [29, p. 150, footnote 30].

  2. 2.

    See [32]. The Faculty wives equipment loan center is a very useful organization. In 1977, when María Manzano was in Berkeley with a Fulbright grant, she was able to loan dishes and sheets from them.

  3. 3.

    In this paragraph, all the quotes are taken from [10].

  4. 4.

    See [32].

  5. 5.

    See [21].

  6. 6.

    In [29, pp. 129–130].

  7. 7.

    In [29, p. 131].

  8. 8.

    See [36].

  9. 9.

    The thesis was never published, but the results were published in several papers; the more directly related are [11], and [12].

  10. 10.

    The second volume, whose index appears in the first, was never published, although some of its chapters were circulated among his students.

  11. 11.

    Probably Church explained in class what was to become his paper [5] on that subject.

  12. 12.

    See [29, p. 142].

  13. 13.

    See [36].

  14. 14.

    In [29, p. 132, footnote 11].

  15. 15.

    In his contribution to this volume (Chap. “A Fortuitous Year with Leon Henkin”), Solomon Feferman explains a little bit The Loyalty Oath, whose main requirement was to force people to declare they were not members of the Communist Party.

  16. 16.

    See [7, pp. 5–6].

  17. 17.

    Personal letter to María Manzano.

  18. 18.

    Explained in his [29].

  19. 19.

    Feferman in [7, pp. 5–6], cites this 1955 letter that Tarski wrote, with Leon Henkin.

  20. 20.

    See [7, pp. 5–6].

  21. 21.

    Personal communication to María Manzano.

  22. 22.

    The whole reference of these problems is included in the Appendix Curriculum vitae of this book.

  23. 23.

    Personal e-mail to María Manzano.

  24. 24.

    In this book we have devoted the chapter Henkin on Completeness to this issue. Therein, we include a section on the completeness proofs Henkin told us in class.

  25. 25.

    Personal communication to María Manzano.

  26. 26.

    See [28, p. 3].

  27. 27.

    See [9, p. 592].

  28. 28.

    See [9, pp. 592–593].

  29. 29.

    See [9, p. 593].

  30. 30.

    See [9, p. 593].

  31. 31.

    See [2, p. 89, footnote 3]. See also Anellis [3].

  32. 32.

    We interchanged several e-mails.

References

  1. Addison, J., et al.:. In Memoriam: Leon Albert Henkin. University of California. Available via http://senate.universityofcalifornia.edu/inmemoriam/leonalberthenkin.html

  2. Anellis, I.: Review of Bertrand Russell, Towards the Principles of Mathematics, 1900–2002, edited by Gregory H. Moore, and Bertrand Russell, Foundations of Logic, 1903–2005 edited by Alasdair Urquhart with the assistance of Albert C. Lewis. Mod. Log. 8(34), 57–93 (2001). http://projecteuclid.org/euclid.rml/1081173771

    Google Scholar 

  3. Anellis, I.: Evaluating Bertrand Russell: The Logician and His Work (2012). Docent Press

    Google Scholar 

  4. Church, A.: The Calculi of Lambda-Conversion. Annals of Mathematical Studies, vol. 6. Princeton University Press, Princeton (1941)

    Google Scholar 

  5. Church, A.: A formulation of the logic of sense and denotation. In: Structure, Methods and Meaning, Essays in Honor of Henry M. Sheffer, New York. pp. 3–24. (1951). Revised in NOUS: vol. 7 (1973), pp. 24–33; vol. 8 (1974), pp. 135–156; and vol. 27 (1993), pp. 141–157

    Google Scholar 

  6. DelVecchio, R.: Leon A. Henkin—Cal math educator. SFGate SF Chronicle. Available via http://www.sfgate.com/default/article/Leon-A-Henkin-Cal-math-educator-2466402.php (2006)

  7. Feferman, S.: Tarski’s conception of logic. Ann. Pure Appl. Log. 126, 5–13 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  8. Goodman, N., Quine, W.V.: Steps toward a constructive nominalism. J. Symb. Log. 12(4), 105–122 (1947)

    Article  MathSciNet  MATH  Google Scholar 

  9. Grattan-Guinness, I.: The Search for Mathematical Roots, 1870–1940: Logics, Set Theories, and the Foundations of Mathematics from Cantor Through Russell to Gödel. Princeton University Press, Princeton (2000)

    Google Scholar 

  10. Henkin, J., Henkin, P., et al.: Many views of Leon Henkin. Manuscript (2006)

    Google Scholar 

  11. Henkin, L.: The completeness of the first-order functional calculus. J. Symb. Log. 14(3), 159–166 (1949)

    Article  MathSciNet  MATH  Google Scholar 

  12. Henkin, L.: Completeness in the theory of types. J. Symb. Log. 15(2), 81–91 (1950)

    Article  MathSciNet  MATH  Google Scholar 

  13. Henkin, L.: Banishing the rule of substitution for functional variables. J. Symb. Log. 18(3), 201–208 (1953)

    Article  MathSciNet  MATH  Google Scholar 

  14. Henkin, L.: Some notes on nominalism. J. Symb. Log. 18(1), 19–29 (1953)

    Article  MathSciNet  MATH  Google Scholar 

  15. Henkin, L.: A generalization of the concept of ω-consistency. J. Symb. Log. 19(3), 183–196 (1954)

    Article  MathSciNet  MATH  Google Scholar 

  16. Henkin, L.: The nominalistic interpretation of mathematical language. Bull. Soc. Math. Belg. 7, 137–141 (1955)

    MathSciNet  Google Scholar 

  17. Henkin, L.: The representation theorem for cylindrical algebras. In: Skolem, Th., Hasenjaeger, G., Kreisel, G., Robinson, A. (eds.) Mathematical Interpretation of Formal Systems, pp. 85–97. North-Holland, Amsterdam (1955)

    Chapter  Google Scholar 

  18. Henkin, L.: A generalization of the concept of ω-completeness. J. Symb. Log. 22(1), 1–14 (1957)

    Article  MathSciNet  MATH  Google Scholar 

  19. Henkin, L.: On mathematical induction. Am. Math. Mon. 67(4), 323–338 (1960)

    Article  MathSciNet  MATH  Google Scholar 

  20. Henkin, L., Smith, W.N., Varineau, V.J., Walsh, M.J.: Retracing Elementary Mathematics. Macmillan, New York (1962)

    MATH  Google Scholar 

  21. Henkin, L.: Are logic and mathematics identical? Science 138, 788–794 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  22. Henkin, L.: New directions in secondary school mathematics. In: Ritchie, R.W. (ed.) New Directions in Mathematics, pp. 1–6. Prentice Hall, New York (1963)

    Google Scholar 

  23. Henkin, L.: An extension of the Craig–Lyndon interpolation theorem. J. Symb. Log. 28(3), 201–216 (1963)

    Article  MathSciNet  Google Scholar 

  24. Henkin, L.: A theory of propositional types. Fundam. Math. 52, 323–344 (1963)

    MathSciNet  MATH  Google Scholar 

  25. Henkin, L.: Mathematical foundations for mathematics. Am. Math. Mon. 78(5), 463–487 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  26. Henkin, L.: Identity as a logical primitive. Philosophia. Philos. Q. Isr. 5(1–2), 31–45 (1975)

    Google Scholar 

  27. Henkin, L.: The logic of equality. Am. Math. Mon. 84(8), 597–612 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  28. Henkin, L.: The roles of action and of thought in mathematics education—one mathematician’s passage. In: Fisher, N.D., Keynes, H.B., Wagreich, Ph.D. (eds.) Changing the Culture: Mathematics Education in the Research Community. CBMS Issues in Mathematics Education, vol. 5, pp. 3–16. Am. Math. Soc. in cooperation with Math. Assoc. of America, Providence (1995)

    Google Scholar 

  29. Henkin, L.: The discovery of my completeness proofs. Bull. Symb. Log. 2(2), 127–158 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  30. Henkin, L., Tarski, A.: Cylindric algebras. In: Dilworth, R.P. (ed.) Lattice Theory. Proceedings of Symposia in Pure Mathematics, vol. 2, pp. 83–113. Am. Math. Soc., Providence (1961). [Reprint, Givant, S.R. and McKenzie, R.N. (eds.) Alfred Tarski. Collected Papers, vol. 4, pp. 647–655, Birkhäuser, Basel (1986)]

    Chapter  Google Scholar 

  31. Henkin, L., Monk, J.D., Tarski, A.: Cylindric Algebras. Part I. Studies in Logic and the Foundations of Mathematics, vol. 64. North-Holland, Amsterdam (1971)

    Google Scholar 

  32. Henkin, P.: Proposed memorial oration. Manuscript (2006)

    Google Scholar 

  33. Monk, J.D.: In memoriam: Leon Albert Henkin. Bull. Symb. Log. 15(3), 326–331 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  34. Quine, W.V.: On universals. J. Symb. Log. 12(3), 75–84 (1947)

    Google Scholar 

  35. Duke’s cuts crowd math dept. The Daily Californian, Monday, August 29, 1983

    Google Scholar 

  36. The Princeton Mathematics Community in the 1930s (PMC14)

    Google Scholar 

  37. The Princeton Mathematics Community in the 1930s (PMC19)

    Google Scholar 

  38. Russell, B., Whitehead, A.: Principia Mathematica, vols. 1–3. Cambridge University Press, Cambridge (1910–1913)

    Google Scholar 

  39. Sanders, R.: Leon Henkin, advocate for diversity in math & sciences, has died. UC Berkeley Press Release. 09 November 2006. Available via http://www.berkeley.edu/news/media/releases/2006/11/09_henkin.shtml

Download references

Acknowledgements

The authors wish to thank several colleagues and staff, including Steve Givant, Peter Andrews, Wilfrid Hodges, John Addison, Antonia Huertas and David Kessler. Special thanks to Henkin’s family: Ginette Henkin, Paul Henkin and Julian Henkin.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to María Manzano .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Manzano, M., Alonso, E. (2014). Leon Henkin. In: Manzano, M., Sain, I., Alonso, E. (eds) The Life and Work of Leon Henkin. Studies in Universal Logic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-09719-0_1

Download citation

Publish with us

Policies and ethics