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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Coding into $K$ by reasonable forcing


Author: Ralf-Dieter Schindler
Journal: Trans. Amer. Math. Soc. 353 (2001), 479-489
MSC (2000): Primary 03E55, 03E15; Secondary 03E35, 03E60
Published electronically: October 11, 2000
MathSciNet review: 1804506
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Abstract:

We present a technique for coding sets ``into $K$,'' where $K$ 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.


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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: http://dx.doi.org/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
Published electronically: 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)
Article copyright: © Copyright 2000 American Mathematical Society