The problem here PL is Jesus said it was Jerusalem - when John called the woman mystery Babylon he's using that figuratively.
Just as he did with the great city:
(Rev 11:8 KJV) And their dead bodies shall lie in the street of the great city, which spiritually is called Sodom and Egypt, where also our Lord was crucified.
If you take the time to read all the "great city" verses in the revelation you will not see John change the identity from "where also our Lord was crucified" to another city.
Once again Locutus, Jerusalem is not Mystery, Babylon the great, the woman who rides the beast. I have already proven this to you but you have not believed it. The short version is that, God puts it into the hearts of the beast and the ten kings to hate the woman, completely destroying her so that no one will ever inhabit her again. Yet, after Satan is released from the Abyss, he gathers those people figuratively called Gog and Magog and they surround the camp of God's people, the city that he loves, which could only be Jerusalem.
That this event takes place at the end of the thousand year period, would demonstrate that Jerusalem will be inhabited during the thousand year reign of Christ all the way up to the end. Since the woman, that great city, is destroyed sometime during the great tribulation period, how then can the woman be Jerusalem? For she is destroyed and uninhabitable and Jerusalem has people living in it throughout the thousand years. Your problem is incomplete exegesis.
The destruction of the woman who rides the beast, that great city during the tribulation:
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"With such violence the great city of Babylon will be thrown down, never to be found again.
* The music of harpists and musicians, pipers and trumpeters, will never be heard in you again.
* No worker of any trade will ever be found in you again.* The sound of a millstone will never be heard in you again.
* The light of a lamp will never shine in you again.
* The voice of bridegroom and bride will never be heard in you again.
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Jerusalem inhabited throughout the entire thousand years to the very end:
"When the thousand years are over, Satan will be released from his prison and will go out to deceive the nations in the four corners of the earth—Gog and Magog—and to gather them for battle. In number they are like the sand on the seashore. They marched across the breadth of the earth and surrounded
the camp of God’s people, the city he loves. But fire came down from heaven and devoured them.
Conclusion: The woman who rides the beast, which is that great city that rules over the kings of the earth, is destroyed during the last 3 1/2 years before Christ returns to the earth to end the age, never to be inhabited ever again. Jerusalem on the other hand, is shown to be inhabited throughout the entire thousand year reign of Christ. Therefore, the woman who rides the beast, that great city, cannot possibly be Jerusalem.