Yosef Karo

“ I am betrothed to you Then nothing has happened even if he was originally speaking with her about marriage-related matters because it is written “when a man take,” not “when he takes himself.”
Seif 7: If she gives him money and she says I am betrothed to you, she is not betrothed.
Seif 8: If he gave her [money] and she speaks [i.e. the engagement formula] , if he was speaking with her about matters of betrothal, it is definitely betrothal, and if not, it is a case of doubtful betrothal. ”

“ And we require asking a sage if a certain person is not considered important so as to permit her to remarry without a get. Rema: And there are those who are stringent, even where she did not say originally when she gave it: “I will be betrothed to you,” rather, she gave it without any statement and he said to her, “Be betrothed to me, etc.” ”