Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:   give an improvement of Vaught's Theorem on Axiomatizability by a Scheme.  show that any RE theory that directly interprets the theory of non-surjective unordered pairing, where pairing need not be functional, is axiomatizable by a scheme.
['Albert Visser']
I am writing a research paper on a idea Vaught's theorem on axiomatizability by a scheme
[{"from": "human", "value": "I am writing a research paper on a idea Vaught's theorem on axiomatizability by a scheme"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:   give an improvement of Vaught's Theorem on Axiomatizability by a Scheme.  show that any RE theory that directly interprets the theory of non-surjective unordered pairing, where pairing need not be functional, is axiomatizable by a scheme."}]