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Insofar as the Marxist view of history holds that class revolution is inevitable and inexorable, this was expected to spread around the world. As such, exporting revolution was a major goal of Communist powers. Lenin was the champion of world revolution and founded the prominent umbrella group, the "Communist International", in 1919.
In your question, the notoriously anti-red Senator Joseph McCarthy seems to have simply added some color to the story by describing the revolutionary process as "enslavement".
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Of course not. I doubt very much if any communist leader would be stupid enough to openly say they want to enslave anyone. America enslaves, of course. But not the other way around. Communism liberates people. (Not my opinion - theirs.)