Skip to main content

Church’s Set Theory with a Universal Set

For Alonzo Church on the occasion of his ninetieth birthday

  • Chapter
Logic, Meaning and Computation

Part of the book series: Synthese Library ((SYLI,volume 305))

Abstract

A detailed and fairly elementary introduction is given to the techniques used by Church to prove the consistency of his set theory with a universal set by constructing models of it from models of ZF. The construction is explained and some general facts about it proved.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Boffa, M., and Pétry, A. 1993 On self-membered sets in Quine’s set theory NF, Logique et Analyse, vol. 141-142, pp. 59–60.

    Google Scholar 

  • Church, A. 1974 Set theory with a universal set, Proceedings of the Tarski symposium, Proceedings of Symposia in Pure Mathematics (L. Henkin, editor), vol. XXV, Providence, pp. 297–308; also in International Logic Review, vol. 15, pp. 11-23.

    Google Scholar 

  • Forster, T. E. 1987 Term models for weak set theories with a universal set, The Journal of Symbolic Logic, vol. 52, pp. 374–387.

    Article  Google Scholar 

  • Forster, T. E. 1995 Set theory with a universal set: Exploring an untyped universe, second edition, Oxford Logic Guides, no. 31, Clarendon Press, Oxford.

    Google Scholar 

  • Forster, T. E., and R. Kaye 1991 End-extensions preserving power set, The Journal of Symbolic Logic, vol. 56, pp. 323–328.8

    Article  Google Scholar 

  • Grishin, V. N. 1969 Consistency of a fragment of Quine’s NF system, Soviet Mathematics Doklady, vol. 10, pp. 1387–1390.

    Google Scholar 

  • Henson, C. W. 1973b Permutation methods applied to NF, The Journal of Symbolic Logic, vol. 38, pp. 69–76.

    Article  Google Scholar 

  • Jensen, R. B. 1969 On the consistency of a slight (?) modification of Quine’s NF, Synthese, vol. 19, pp. 250–263.

    Article  Google Scholar 

  • Körner, F. 1994 Cofinal indiscernibles and some applications to New Foundations, Mathematical Logic Quarterly, vol. 40, pp. 347–356.

    Article  Google Scholar 

  • Mitchell, E. 1976 A model of set theory with a universal set, Ph.D. thesis, Madison, Wisconsin.

    Google Scholar 

  • Oswald, U. 1976 Fragmente von “New Foundations” und typentheorie, Ph.D. thesis, ETH, Zürich, 46 pp.

    Google Scholar 

  • Scott, D. S. 1962 Quine’s individuals, Logic, Methodology and Philosophy of Science (E. Nagel, editor), Stanford University Press, pp. 111–115.

    Google Scholar 

  • Tarski, A. 1986 What are logical notions?, History and Philosophy of Logic, vol. 7, pp. 143–154.

    Article  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Forster, T. (2001). Church’s Set Theory with a Universal Set. In: Anderson, C.A., Zelëny, M. (eds) Logic, Meaning and Computation. Synthese Library, vol 305. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0526-5_4

Download citation

  • DOI: https://doi.org/10.1007/978-94-010-0526-5_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-3891-1

  • Online ISBN: 978-94-010-0526-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics