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proper forcing; large cardinals
We show that in the presence of large cardinals proper forcings do not change the theory of $L(\Bbb R)$ with real and ordinal parameters and do not code any set of ordinals into the reals unless that set has already been so coded in the ground model.
[BJW] Beller A., Jensen R.B., Welch P.: Coding the Universe. Oxford University Press Oxford (1985). MR 0645538
[FM] Foreman M., Magidor M.: Large cardinals and definable counterexamples to the continuum hypothesis. Ann. Pure Appl. Logic 76 (1995), 47-97. MR 1359154 | Zbl 0837.03040
[FMS] Foreman M., Magidor M., Shelah S.: Martin's Maximum, saturated ideals and nonregular ultrafilters. Ann. Math. 127 (1988), 1-47. MR 0924672 | Zbl 0645.03028
[HV] Hájek P., Vopěnka P.: The Theory of Semisets. North Holland Amsterdam (1972). MR 0289286
[J] Jech T.: Set Theory. (1978), Academic Press New York. MR 0506523 | Zbl 0419.03028
[JMMP] Jech T., Magidor M., Mitchell W.J., Prikry K.: Precipitous ideals. J. Symbolic Logic 45 (1980), 1-8. MR 0560220 | Zbl 0437.03026
[M] Moschovakis Y.N.: Descriptive Set Theory. (1980), North Holland Amsterdam. MR 0561709 | Zbl 0433.03025
[MS] Martin D.A., Steel J.R.: A proof of projective determinacy. J. Amer. Math. Soc. 2 71-125 (1989). MR 0955605 | Zbl 0668.03021
[NZ] Neeman I., Zapletal J.: Proper forcing and $L(\Bbb R)$. J. London Math. Soc. submitted.
[S] Schimmerling E.: handwritten notes of W.H. Woodin's lectures.
[Sh] Shelah S.: Proper Forcing. Springer Verlag Berlin (1981), Lecture Notes in Math. 940. MR 0675955
[W1] Woodin W.H.: Supercompact cardinals, sets of reals and weakly homogeneous trees. Proc. Natl. Acad. Sci. USA 85 (1988), 6587-6591. MR 0959110 | Zbl 0656.03037
[W2] Woodin W.H.: The axiom of determinacy, forcing axioms and the nonstationary ideal. to appear. MR 1713438 | Zbl 0954.03046
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