Two consequences of determinacy consistent with choice

Steel, John R.; Van Wesep, Robert

doi:10.1090/S0002-9947-1982-0656481-5

Two consequences of determinacy consistent with choice
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by John R. Steel and Robert Van Wesep PDF

Trans. Amer. Math. Soc. 272 (1982), 67-85 Request permission

Abstract:

We begin with a ground model satisfying ${\text {ZF}} + {\text {AD}} + {\text {A}}{{\text {C}}_{\mathbf {R}}}$, and from it construct a generic extension satisfying ${\text {ZFC}} + {\mathbf {\delta }}_2^1 = {\omega _2} +$ "the nonstationary ideal on ${\omega _1}$ is ${\omega _2}$-saturated".

References

On the compactness of

and

43

Leo Harrington, Analytic determinacy and $0^{\sharp }$, J. Symbolic Logic 43 (1978), no. 4, 685–693. MR 518675, DOI 10.2307/2273508
Alexander S. Kechris, $\textrm {AD}$ and projective ordinals, Cabal Seminar 76–77 (Proc. Caltech-UCLA Logic Sem., 1976–77) Lecture Notes in Math., vol. 689, Springer, Berlin, 1978, pp. 91–132. MR 526915
Kenneth Kunen, Saturated ideals, J. Symbolic Logic 43 (1978), no. 1, 65–76. MR 495118, DOI 10.2307/2271949
Yiannis N. Moschovakis, Determinacy and prewellorderings of the continuum, Mathematical Logic and Foundations of Set Theory (Proc. Internat. Colloq., Jerusalem, 1968) North-Holland, Amsterdam, 1970, pp. 24–62. MR 0280362
William Mitchell, Hypermeasurable cardinals, Logic Colloquium ’78 (Mons, 1978) Studies in Logic and the Foundations of Mathematics, vol. 97, North-Holland, Amsterdam-New York, 1979, pp. 303–316. MR 567676
Robert M. Solovay, The independence of DC from AD, Cabal Seminar 76–77 (Proc. Caltech-UCLA Logic Sem., 1976–77) Lecture Notes in Math., vol. 689, Springer, Berlin, 1978, pp. 171–183. MR 526918
Robert Van Wesep, Wadge degrees and descriptive set theory, Cabal Seminar 76–77 (Proc. Caltech-UCLA Logic Sem., 1976–77) Lecture Notes in Math., vol. 689, Springer, Berlin, 1978, pp. 151–170. MR 526917