If the cold war turned into an armed military conflict between the united states and the soviet union, it will be a Hegemonic War.
The Cold War, which started after World War II, was a time of geopolitical conflict between the United States, the Soviet Union, and their respective allies, the Western Bloc and the Eastern Bloc. Competition between the USSR and the US escalated as World War II changed both countries, making them strong global powers. After the Axis powers were defeated, a political and ideological conflict between the US and the USSR gave place to the beginning of the Cold War.
Global war, often known as "hegemonic conflict," by definition produces a new hegemon in order to establish a new system. With their own set of preferences, this new hegemon will design the new global order. A global conflict like the hegemons is to maintain the newly established order, just like in a world war.
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