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Another Use of Set Theory

Published online by Cambridge University Press:  15 January 2014

Patrick Dehornoy
Patrick Dehornoy*
Affiliation:
Mathématiques, Université Decaen, 14032 CAEN, France. E-mail: dehornoy@math.unicaen.fr
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Abstract

Here, we analyse some recent applications of set theory to topology and argue that set theory is not only the closed domain where mathematics is usually founded, but also a flexible framework where imperfect intuitions can be precisely formalized and technically elaborated before they possibly migrate toward other branches. This apparently new role is mostly reminiscent of the one played by other external fields like theoretical physics, and we think that it could contribute to revitalize the interest in set theory in the future.

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 2 , Issue 4 , December 1996 , pp. 379 - 391
Copyright
Copyright © Association for Symbolic Logic 1996

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References

REFERENCES

[1] Atiyah, M., The Jones-Witten invariants of knots, Séminaire Bourbaki (1989), exposé 715.Google Scholar
[2] Barwise, K. J. (editor), Handbook of mathematical logic, North-Holland, 1977.Google Scholar
[3] Dehornoy, P., A fast method for comparing braids, Advances in Mathematics, to appear.Google Scholar
[4] Dehornoy, P., -complete families of elementary sequences, Annals of Pure and Applied Logic, vol. 38 (1988), pp. 257–287.CrossRefGoogle Scholar
[5] Dehornoy, P., Braid groups and left distributive operations, Transactions of the American Mathematical Society, vol. 345 (1994), no. 1, pp. 115–151.CrossRefGoogle Scholar
[6] Dehornoy, P., From large cardinals to braids via distributive algebra, Journal of Knot Theory and its Ramifications, vol. 4 (1995), no. 1, pp. 33–79.CrossRefGoogle Scholar
[7] Dougherty, R. and Jech, T., Finite left-distributive algebras and embedding algebras, Advances in Mathematics, to appear.Google Scholar
[8] Friedman, H., Higher set theory and mathematical practice, Annals of Mathematical Logic, vol. 2 (1971), pp. 325–357.CrossRefGoogle Scholar
[9] Friedman, H., On the necessary use of abstract set theory, Advances in Mathematics, vol. 41 (1981), pp. 209–280.CrossRefGoogle Scholar
[10] Kanamori, A., The higher infinite, Springer-Verlag, 1994.Google Scholar
[11] Kauffman, L., Knots and physics, World Scientific, 1991.CrossRefGoogle Scholar
[12] Kirby, L. and Paris, J., Accessible independence results for Peano arithmetic, Bulletin of the London Mathematical Society, vol. 14 (1982), pp. 285–293.CrossRefGoogle Scholar
[13] Lane, S. Mac, Is Mathias an ontologist?, Set theory of the continuum (Judah, , Just, , and Woodin, , editors), Springer-Verlag, 1992, MSRI Publ. 26, pp. 119–122.CrossRefGoogle Scholar
[14] Larue, D., On braid words and irreflexivity, Algebra Universalis, vol. 31 (1994), pp. 104–112.CrossRefGoogle Scholar
[15] Laver, R., The left distributive law and the freeness of an algebra of elementary embed-dings, Advances in Mathematics, vol. 91 (1992), no. 2, pp. 209–231.CrossRefGoogle Scholar
[16] Laver, R., On the algebra of elementary embeddings of a rank into itself, Advances in Mathematics, vol. 110 (1995), pp. 334–346.CrossRefGoogle Scholar
[17] Martin, D. A. and Steel, J., A proof ofprojective determinacy, Journal of the American Mathematical Society, vol. 2 (1989), pp. 71–125.CrossRefGoogle Scholar
[18] Mathias, A. R. D., What is Mac Lane missing?, Set theory of the continuum (Judah, , Just, , and Woodin, , editors), Springer-Verlag, 1992, MSRI Publ. 26, pp. 119–122.Google Scholar
[19] Roitman, J., The uses of set theory, Mathematical Intelligencer, vol. 14 (1992), no. 1, pp. 63–69.CrossRefGoogle Scholar
[20] Shelah, S., Can you take Solovay's inacessible away?, Israel Journal of Mathematics, vol. 48 (1984), pp. 1–47.CrossRefGoogle Scholar
[21] Solovay, R., Reinhardt, W., and Kanamori, A., Strong axioms of infinity and elementary embeddings, Annals of Mathematical Logic, vol. 13 (1978), pp. 73–116.CrossRefGoogle Scholar
[22] Woodin, H., Large cardinal axioms and independence: the continuum problem revisited, Mathematical Intelligencer, vol. 16 (1994), no. 3, pp. 31–35.Google Scholar
[23] Woodin, H., Solovay, R., and Mathias, A., The axiom of determinacy, to appear.Google Scholar