Let your women keep silent in the churches, for they are not permitted to speak; but they are to be submissive, as the law also says.
1 Corinthians 14:34

Since there is no Old Testament law requiring that women do not speak, Paul clearly is not referencing biblical law. If not biblical law, what is Paul talking about? The only answer that makes sense is that he's referring to a man-made law that the folks in Corinth are aware of - perhaps there's a city-wise ban on women speaking in public places. However, it isn't a biblical law. Therefore, Paul's statement is a cultural one - he's talking the folks in Corinth to keep their women silent, just as the laws of the city of Corinth require (Paul also speaks of obeying the governing authorities). Paul's reference to submission is from the biblical law, so his statement about "as the law also says" simply joins the notion of submission in the biblical law and the man-made law that covers Corinth.

In a land that does not require that women remain silent in public, Paul's statement to the Corinthians about women being silent in church does not apply.