Why not γίνεται?
Να γίνεται is the continuous subjunctive and would be translated "the woman wants to be becoming doctor" continuously becoming doctor again and again.
Thanks, I am beginning to grasp this now. Just like in Bulgarian. But the aspect system (imperfective and perfect aspects) seems to be more comprehensive in Slavic languages.
Off the grammar topic: does η γυναίκα sound in Greek a bit derogative as it does in English or not? In English you wouldn't say about someone "the woman" but rather"the lady"...
In general yes, it's the same. But in Greek you may also use this sentence in another way with the right intonation and it would mean something along the lines of "She wants to become a doctor, don't you see/can't you understand?"
Thank you, that's good to know. And of course intonation and context makes all the difference, as probably in every language!