MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).

## Return to Answer

2 Fixed Jech reference.

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.

1

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.