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World-systems analysis is a well-established but poorly-defined critical research tradition in the social sciences. Its undisputed progenitor, Immanuel Wallerstein, steadfastly maintains that world-systems analysis is not a theory, yet it is widely referred to as such by commentators, critics, and practitioners alike. The resolution to this conundrum is to identify the defining elements of world-systems analysis as a perspective for understanding human society, then to evaluate propositions based on these defining elements as theories that have been conceptualized from a world-systems perspective. In this presentation five defining elements of world-systems analysis are identified that together support a central theorem that the core-periphery hierarchy of the modern world-system can best be understood in terms of state strength and cultural integration. A further conjecture is made that the successor world-system to the current capitalist world-economy is more likely to be an American world-polity than the socialist world-government craved by many world-systems analysts. A concluding slide links to my recent characterization of the American world-system as an American Tianxia, drawing on terminology from Chinese international relations theory to describe the American-centered world today.