Skip to main content
SpringerLink
Log in

On Several Continuum Hypotheses

  • Chapter
Aspects of Mathematical Logic

Part of the book series: C.I.M.E. Summer Schools ((CIME,volume 48))

Abstract

The classical Cantor's continuum hypothesis states that for every infinite set S the cardinality of the set PS of all the subsets of S is the immediate follower of the cardinality kS of S.i.e.

$$ {\text{kPS}} = \left( {{\text{k}}\,{\text{S}}} \right) $$

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

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 16.99
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. Cantor, G. Gesammelte Abhadlungen, Berlin (1932) 8+486.

    Google Scholar 

  2. The independence of the continuum hypothesis. Proc. Nat. Acad. Sci. Usa, 50(1963) 1143–1148;

    Article  Google Scholar 

  3. II Part, Ibidem 51(1964) 105–110.

    Article  Google Scholar 

  4. Set theory and the continuum hypothesis, New York-Amsterdam, (1966) 4+154.

    MATH  Google Scholar 

  5. Gödel, K. The consistency of the axioms of choice and of the generalized continuum hypothesis (Proc. Nat. Ac. Sci. USA 24(1938) 556–557).

    Article  Google Scholar 

  6. The consistency of the axiom of choice and of the generalized continuum hypothesis with the axioms of set theory Princeton, N. J., (1940) 4+69.

    Google Scholar 

  7. Hilbert, D. “Uber das Unendliche, Math. Annalen, 95(1925)161–190.

    MathSciNet  MATH  Google Scholar 

  8. Kurepa, D. Ensembles ordonnés et ramifiés. Thése, Paris, 1935. Publ. math. Belgrad, 4(1935)1–138.

    MathSciNet  MATH  Google Scholar 

  9. L'hypothèse de ramification, comptes rendus 202, 1936. 185–187.

    Google Scholar 

  10. L'hypothèse du continu et les ensembles partiellement of-donnés, Comptes rendus, Paris, 205 (1937) 1196–1198.

    Google Scholar 

  11. Sur une hypothèse de la théorie des ensembles, Comptes rendus, Paris,256(1953) 56+−565 (séance du 09.02.1953.

    Google Scholar 

  12. Sur un principe de la théorie des espaces abstraits, Ibidem 655–657 (séance du 16.02.1953).

    Google Scholar 

  13. Sull'ipotesi del continuo, Rendiconti del Seminario Matematico, Torino, 18, 1958–59, 11–20.

    MathSciNet  Google Scholar 

  14. Sur une proposition de la théorie des ensembles, C.r.Sci. Paris 249 (1959) 2689–99.

    MathSciNet  Google Scholar 

  15. Mathias A.R.D. A survey of recent results in set theory 11+76 (Stanford university, 1968).,

    Google Scholar 

  16. Sierpiński, W. Hypothèse du continu, Warszawa-Lwow 1934, 6+192.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Beograd, Serbia

    Djurio Kurepa

Authors
  1. Djurio Kurepa
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

E. Casari (Coordinator)

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Kurepa, D. (2010). On Several Continuum Hypotheses. In: Casari, E. (eds) Aspects of Mathematical Logic. C.I.M.E. Summer Schools, vol 48. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11080-1_2

Download citation

Publish with us

Policies and ethics

Search

Navigation