Transactions of the American Mathematical Society

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
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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.

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

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

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