Skip to main content
Log in

Projective Well-orderings of the Reals

  • Published:
Archive for Mathematical Logic Aims and scope Submit manuscript

Abstract

If there is no inner model with ω many strong cardinals, then there is a set forcing extension of the universe with a projective well-ordering of the reals.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Caicedo, A. Simply definable well-orderings of the reals. PhD Dissertation, Department of Mathematics, University of California (2003)

  2. Harrington L. (1977) Long projective well-orderings. Ann. Math. Logic 12(1): 1–24

    Article  MATH  MathSciNet  Google Scholar 

  3. Hauser K. (1995) The consistency strength of projective absoluteness. Ann. Pure Appl. Logic 74(3): 245–295

    Article  MATH  MathSciNet  Google Scholar 

  4. Hauser K., Hjorth G. (1997) Strong cardinals in the core model. Ann. Pure Appl. Logic 83(2): 165–198

    Article  MATH  MathSciNet  Google Scholar 

  5. Hauser K., Schindler R. (2000) Projective uniformization revisited. Ann. Pure Appl. Logic 103(1–3): 109–153

    Article  MATH  MathSciNet  Google Scholar 

  6. Kunen K. (1980) Set Theory. An Introduction to Independence Proofs. Elsevier, Amsterdam

    MATH  Google Scholar 

  7. Mansfield R. (1975) The non-existence of a \(\Sigma^1_2\) well-ordering of the Cantor set. Fundam. Math. 86(3): 279–282

    MATH  MathSciNet  Google Scholar 

  8. Mitchell W., Schimmerling E. (1995) Covering without countable closure. Math. Res. Lett. 2(5): 595–609

    MATH  MathSciNet  Google Scholar 

  9. Mitchell W., Schimmerling E., Steel J. (1997) The covering lemma up to a Woodin cardinal. Ann. Pure Appl. Logic 84(2): 219–255

    Article  MATH  MathSciNet  Google Scholar 

  10. Mitchell W., Steel J. (1994) Fine Structure and Iteration Trees. Springer, Berlin Heidelberg New York

    MATH  Google Scholar 

  11. Schindler R. (2001) Coding into K by reasonable forcing. Trans. Am. Math. Soc. 353(2): 479–489

    Article  MATH  MathSciNet  Google Scholar 

  12. Schindler R. (2002) The core model for almost linear iterations. Ann. Pure Appl. Logic 116(1–3): 205–272

    Article  MATH  MathSciNet  Google Scholar 

  13. Steel, J. The derived model theorem. (Unpublished manuscript)

  14. Steel J. (1996) The Core Model Iterability Problem. Springer, Berlin Heidelberg New York

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Andrés Eduardo Caicedo.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Caicedo, A.E., Schindler, R. Projective Well-orderings of the Reals. Arch. Math. Logic 45, 783–793 (2006). https://doi.org/10.1007/s00153-006-0002-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00153-006-0002-6

Keywords

Mathematics Subject Classification (2000)

Navigation