Should it be "I have a wife."?
Wife is "σύζυγος" in Greek. Although the meaning of the sentence is "I have a wife" if you say that in an everyday conversation.
Wife is γυναίκα in Greek. Σύζυγος is spouse, which is used for both husband and wife, exactly like in English.
Well if you say "η γυναίκα μου" you always mean my wife. But wife does not translate to "γυναίκα" in any other concept. But it can always be translated as "η σύζυγος".
Yes, that is true, I was only referring to the closest word match between the two languages. I'm not sure why "I have a woman." is given as a practice sentence here as its obvious meaning ("I own a woman") is crass.
Well, that's true. :)