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2 | Fixed Jech reference. | ||
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Solovay proved that ZF+AD implies that $\omega_1$ and $\omega_2$ are measurable, in the mid-1960s, but his proofs were not published at the time. Simpler proofs were given by other people. A proof for $\omega_1$ may be found in Moschovakis's Descriptive Set Theory, the 2nd edition of which is available for free here. I expect that both Both results are in Jech's Set Theory, 3rd edition, pp. 633--636. |
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Solovay proved that ZF+AD implies that $\omega_1$ and $\omega_2$ are measurable, in the mid-1960s, but his proofs were not published at the time. Simpler proofs were given by other people. A proof for $\omega_1$ may be found in Moschovakis's Descriptive Set Theory, the 2nd edition of which is available for free here. I expect that both results are in Jech's Set Theory. |
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