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.
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Caicedo, A. Simply definable well-orderings of the reals. PhD Dissertation, Department of Mathematics, University of California (2003)
Harrington L. (1977) Long projective well-orderings. Ann. Math. Logic 12(1): 1–24
Hauser K. (1995) The consistency strength of projective absoluteness. Ann. Pure Appl. Logic 74(3): 245–295
Hauser K., Hjorth G. (1997) Strong cardinals in the core model. Ann. Pure Appl. Logic 83(2): 165–198
Hauser K., Schindler R. (2000) Projective uniformization revisited. Ann. Pure Appl. Logic 103(1–3): 109–153
Kunen K. (1980) Set Theory. An Introduction to Independence Proofs. Elsevier, Amsterdam
Mansfield R. (1975) The non-existence of a \(\Sigma^1_2\) well-ordering of the Cantor set. Fundam. Math. 86(3): 279–282
Mitchell W., Schimmerling E. (1995) Covering without countable closure. Math. Res. Lett. 2(5): 595–609
Mitchell W., Schimmerling E., Steel J. (1997) The covering lemma up to a Woodin cardinal. Ann. Pure Appl. Logic 84(2): 219–255
Mitchell W., Steel J. (1994) Fine Structure and Iteration Trees. Springer, Berlin Heidelberg New York
Schindler R. (2001) Coding into K by reasonable forcing. Trans. Am. Math. Soc. 353(2): 479–489
Schindler R. (2002) The core model for almost linear iterations. Ann. Pure Appl. Logic 116(1–3): 205–272
Steel, J. The derived model theorem. (Unpublished manuscript)
Steel J. (1996) The Core Model Iterability Problem. Springer, Berlin Heidelberg New York
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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
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DOI: https://doi.org/10.1007/s00153-006-0002-6