Coding into $K$ by reasonable forcing
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- by Ralf-Dieter Schindler PDF
- Trans. Amer. Math. Soc. 353 (2001), 479-489 Request permission
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.References
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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
- 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)
- © Copyright 2000 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 353 (2001), 479-489
- MSC (2000): Primary 03E55, 03E15; Secondary 03E35, 03E60
- DOI: https://doi.org/10.1090/S0002-9947-00-02636-2
- MathSciNet review: 1804506