What kind of relationship do Jack Worthing and Gwendolen Fairfax form?

Gwendolen falls in love with Jack (pretending to be Ernest).  She wants to marry a man named Ernest because that man should be able to live up to his name.  He also wants to marry her, but he cannot since his name is not Ernest; thus he would have to reveal his deception and thus show that he does not live up to hi name which she has been so trusting of.