The Jerusalem Talmud was compiled in the 5th century AD and the Babylonian one in the 6th century. Both way after the time of Sha'ul ( Paul). When Paul speaks of the law, he speaks of the Torah.
The Torah was given not only to men, but to women and children also.
"Gather the people together, men, and women, and children, and thy stranger that is within thy gates, that they may hear, and that they may learn, and fear the LORD your God, and observe to do all the words of this law." Deuteronomy 31:12
The gospels record so much about women! Women are mentioned in the genealogy of Matthew plus it is the actual genealogy of Mary given in Luke! Women are portrayed as humble and eager to learn of Yeshua, like Joanna and Mary, dear Mary who 'chose the good part' and learned at Yeshua's feet instead of fretting over the housework. (Luke 10:40-42) It was to a Samaritan woman Yeshua revealed He was Messiah (Yochanan/John 4) and with great compassion Yeshua healed the woman with the serious issue of blood -- even encouraging her great faith; (Luke 8:43-48) Yeshua also healed the daughter of the Canaanite woman whom His disciples had sought to send away. (Mathew 15:20-28). Women were indeed touched by Yeshua's message and believed; no wonder it was women who came to his tomb with spices and discovered the greatest miracle of all: the tomb was empty!
Now having said that, how can we understand passages ( like the one above) used to diminish a woman's role within the body of Yeshua?
As with all of Sha'ul's letters, we have the answer but not the original question he is answering. Our job then becomes one of figuring out what the question may have been. The only thing we can be absolutely sure of is that at least one Corinthian in the assembly wrote Sha'ul about some problem of disturbance in the assembly from a portion of the women. There are three possibilities of what had happened we could guess from Sha'ul's reply.
"Let your women keep silence in the churches: for it is not permitted unto them to speak; but they are commanded to be under obedience, as also saith the law. And if they will learn any thing, let them ask their husbands at home: for it is a shame for women to speak in the church." 1 Corinthians 14:34
Scenario 1) Sha'ul is acknowledging these women have caused a disturbance by interupting the assembly with questions, and Sha'ul is ruling that these women should stop disturbing the assembly and keep quiet until they get home.
Scenario 2) Sha'ul is debunking the men's complaint by first quoting the solution they proposed in their letter to him (their solution being that "women keep quiet") and then Sha'ul challenges their solution with "what? did the Word of G-d come to you only"(vs36); meaning, 'do you men actually believe that G-d only gives His Word for men to share and not women?' In which case the answer is 'no' and women may continue the behaviour the men complained about.
Scenario 3) The whole issue is strictly a tongues issue, and that perhaps some women were speaking out of turn and disturbing the entire meeting. With this view, Sha'ul tells them 'not to forbid speaking in tongues' (vs39) but only try harder to maintain order.(vs40)
Keep in mind that this Corinthian passage is dealing with a specific problem in the Corinthian church. It was never intended to be taken out of context and thrown at any woman who dares open her mouth!
I think he is speaking of this:
"But I would have you know, that the head of every man is Christ; and the head of the woman is the man; and the head of Christ is God."
1 Corinthians 11:3