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In this paper we propose an axiomatization for the notion of strong emergencephenomenon between field theories depending on additional parameters, which wecall parameterized field theories. We present sufficient conditions ensuringthe existence of such phenomena between two given Lagrangian theories. Moreprecisely, we prove that a Lagrangian field theory depending linearly on anadditional parameter emerges from every multivariate polynomial theoryevaluated at differential operators which have well-defined Green functions(or, more generally, that has a right-inverse in some extended sense). As amotivating example, we show that the phenomenon of gravity emerging fromnoncommutativy, in the context of a real or complex scalar field theory, can berecovered from our emergence theorem. We also show that, in the same context,we could also expect the reciprocal, i.e., that noncommutativity could emergefrom gravity. Some other particular cases are analyzed.

An Axiomatization Proposal and a Global Existence Theorem for Strong Emergence Between Parameterized Lagrangian Field Theories