Yosef Karo

“ A betrothed woman is considered as a man's wife in that if another lies with her, they will be guilty of adultery and she would need a divorce in order to marry another man.
סעיף ג –
Paragraph 4 – The woman is betrothed in 3 ways; with money, a document or with intimate relations, as learned from the Torah, but our sages prohibited betrothal by having relations because of impropriety, and if they transgressed this and he betrothed her with relations, he receives rabbinically decreed whiplashes and she is still betrothed. ”

“ Even if he lies with her with the intent of marriage, mutually agreed between him and her, she is not considered as his wife and even if she dedicated herself only for him, rather the opposite is true and he must be forced (by Beis Din) to send her away from his home. ”