Transactions of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6850(e) ISSN 0002-9947(p)

Coding into by reasonable forcing

Author(s): Ralf-Dieter Schindler
Journal: Trans. Amer. Math. Soc. 353 (2001), 479-489.
MSC (2000): Primary 03E55, 03E15; Secondary 03E35, 03E60
Posted: October 11, 2000
MathSciNet review: 1804506
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract:

We present a technique for coding sets ``into ,'' where is the core model below a strong cardinal. Specifically, we show that if there is no inner model with a strong cardinal then any $X\subset\omega_1$ can be made $\boldsymbol{\Delta}^1_3$ (in the codes) in a reasonable and stationary preserving set generic extension.

References:

1.: Beller, A., Jensen, R., and Welch, Ph., Coding the universe, Cambridge 1982. MR 84b:03002
2.: Foreman, M., and Magidor, M., Large cardinals and definable counterexamples to the continuum hypothesis, Ann. Pure Appl. Logic 76 (1995), pp. 47 - 97. MR 96k:03124
3.: Jech, T., Set theory, San Diego 1978. MR 80a:03062
4.: Jensen, R., The core model for non-overlapping extender sequences, handwritten notes.
5.: Neeman, I., and Zapletal, J., Proper forcing and $L({\mathbb{R} })$ , preprint.
6.: -, Proper forcing and absoluteness in $L({\mathbb{R} })$ , Comment. Math. Univ. Carolinae 39 (1998), pp. 281 - 301. CMP 99:03
7.: Schindler, R.-D., Proper forcing and remarkable cardinals, to appear.
8.: Shelah, S., Proper forcing, Springer-Verlag 1982. MR 84h:03042
9.: -, and Stanley, L., Coding and reshaping when there are no sharps, in: ``Set theory of the continuum," Judah, H., et al. (eds.), Springer Verlag 1992, pp. 407 - 416. MR 94m:03083
10.: Steel, J., The core model iterability problem, Springer Verlag 1996. MR 99k:03043
11.: -, Core models with more Woodin cardinals, preprint.
12.: -, and Welch, P., $\Sigma^1_3$ -absoluteness and the second uniform indiscernible, Israel Journal of Mathematics 104 (1998), pp. 157 - 190. MR 99d:03044
13.: Welch, P., Doing without determinacy, in: ``Proc. Logic Colloq. 86, Drake and Truss (eds.), North Holland 1988, pp. 333 - 342. MR 88k:03104
14.: -, Some descriptive set theory and core models, Ann. Pure Appl. Logic 39 (1988), pp. 273 - 290. MR 90d:03095

Similar Articles:

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 03E55, 03E15, 03E35, 03E60

Retrieve articles in all Journals with MSC (2000): 03E55, 03E15, 03E35, 03E60

Additional Information:

Ralf-Dieter Schindler
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
Address at time of publication: Institut für formale Logik, Universität Wien, 1090 Wien, Austria
Email: rds@logic.univie.ac.at

DOI: 10.1090/S0002-9947-00-02636-2
PII: S 0002-9947(00)02636-2
Keywords: Set theory, descriptive set theory, proper forcing, large cardinals.
Received by editor(s): April 24, 1998
Posted: October 11, 2000
Additional Notes: The author would like to thank Itay Neeman, Philip Welch, and Sy Friedman for their interest and for their many hints and comments. John Steel even provided a crucial subclaim, and again I do say thanks for his intellectual support during my stay in Berkeley. I gratefully acknowledge financial support from the Deutsche Forschungsgemeinschaft (DFG)
Copyright of article: Copyright 2000, American Mathematical Society

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|