Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  contains a corrected proof that the statement “every non-empty closed subset of a compact complete separable metric space is separably closed” implies the arithmetical comprehension axiom of reverse mathematics.
['Jeffry L. Hirst']
I am writing a research paper on a idea Reverse mathematics of separably closed sets
[{"from": "human", "value": "I am writing a research paper on a idea Reverse mathematics of separably closed sets"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  contains a corrected proof that the statement \u201cevery non-empty closed subset of a compact complete separable metric space is separably closed\u201d implies the arithmetical comprehension axiom of reverse mathematics."}]