A man gave his wife a get. He then soon afterwards engaged in sexual intercourse with her. Would he be required to give another get?
Possible reasons are that either
The Mishnah in Gittin 81a (Art Scroll 81a3) says that if a man divorced his wife and they were secluded together, then Bais Shammai says that he does not have to give her another get. Bais Hillel says that he must give her another get.
Art Scroll page 81a3 note 22 states that
Bais Hillel is concerned that they cohabited together with the intent of marriage.
This implies that while the get was valid, the cohabitation does cause them to be married.
The gemara on 81b (Art Scroll 81b1) discusses if the witnesses saw that they had relations or not. One possibility is that Bais Shammai holds that the husband did not intend to become remarried while
Bais Hillel hold that a man will not perform his act of cohabitation as a non-marital cohabitation
The conclusion of the gemara however is that both agree with that but the machlokes is in the case that the witnesses to the seclusion did not actually see the cohabitation.
Bais Shammai hold that we do not say that the witnesses to seclusion are in effect witnesses to cohabitation.
Bais Hillel hold that we say that witnesses to seclusion are in effect witnesses to cohabitation.
This implies that if it is known that they had cohabitation, they would be remarried.
Also note that even according to the initial assumption, since the halacha is like Bais Hillel, they would be considered remarried.
There is a question amongst contempory poskim if psychological metzius outlined by the gemara has changed. For example, the Rav is very strongly opposed to the idea that we no longer say tav lemeitav tan du milemeitav armelu because independant career minded women are perfectly happy not to get married.
On the other hand, as the Ran says at the beginning of succah, vechi yecholim anu lehachish es humachash, and there is a wide agreement on the acceptability of free sex.
A friend of a friend had just finished having sex with his girlfriend, and took her out to a Starbucks 3am motzei shabbos. She declined milk in her coffee because, she said, she was makpid on chalav yisrael. However she obviously wasn't makpid on being nivalah beilas znus.
It would seem imho that it is incredibly unlikely that we can apply to the sevara of ein adam oseh beilaso beilas zenus to the scenario you mentioned. I.e. we have no indication from their intercourse that they wish to renew their marital status.
