[Campion]

None of the "Babylonian Talmud" was written in the city of Babylon, for the simple reason that it was not a city anymore at that time. The rabbinic schools from which it came were called, generically, "Babylonian," because they were in Iraq.

A good overview of the history is here. It lists the individual schools and the towns where they were located, which don't include Babylon.

[Uncle Chip]

The "Babylonian Talmud" was written and studied in the schools such as at Pembeditha, but it was not called the Pembeditha Talmud, or the Mesopotamian Talmud, but the Babylonian Talmud.

The Greeks called the area of Babylon "Mesopotamia", but the Jews called the area of Mesopotamia "Babylon". And if you notice on the day of Pentecost in Jerusalem, there are Jews there in Jerusalem from Mesopotamia. "Babylon" had been an empire not just a city. It was Mesopotamia as well --- the land between the rivers and there were a lot of people there.

And by the way, the Iraqi Church might not have a tradition of having been founded by the apostle Peter [no one said they did, especially if it was founded shortly after 30 AD by those Jews there in Jerusalem on the day of Pentecost from Mesopotamia], but they do have a copy of the letter postmarked from there by the apostle Peter in their Bibles, don't they?