Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  show that Shelah cardinals are preserved under the canonical \({{\mathrm{GCH}}}\) forcing notion.  also show that if \({{\mathrm{GCH}}}\) holds and \(F:{{\mathrm{REG}}}\rightarrow {{\mathrm{CARD}}}\) is an Easton function which satisfies some ak properties, then there exists a cofinality preserving generic extension of the universe which preserves Shelah cardinals and satisfies \(\forall \kappa \in {{\mathrm{REG}}},~ 2^{\kappa }=F(\kappa )\). This gives a partial ansr to a question asked by Cody (Arch Math Logic 52(5–6):569–591, 2013) and independently by Honzik (Acta Univ Carol 1:55–72, 2015).  also prove an indestructibility result for Shelah cardinals.
['Mohammad Golshani']
I am writing a research paper on a idea An Easton like theorem in the presence of Shelah cardinals
[{"from": "human", "value": "I am writing a research paper on a idea An Easton like theorem in the presence of Shelah cardinals"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  show that Shelah cardinals are preserved under the canonical \\({{\\mathrm{GCH}}}\\) forcing notion.  also show that if \\({{\\mathrm{GCH}}}\\) holds and \\(F:{{\\mathrm{REG}}}\\rightarrow {{\\mathrm{CARD}}}\\) is an Easton function which satisfies some ak properties, then there exists a cofinality preserving generic extension of the universe which preserves Shelah cardinals and satisfies \\(\\forall \\kappa \\in {{\\mathrm{REG}}},~ 2^{\\kappa }=F(\\kappa )\\). This gives a partial ansr to a question asked by Cody (Arch Math Logic 52(5\u20136):569\u2013591, 2013) and independently by Honzik (Acta Univ Carol 1:55\u201372, 2015).  also prove an indestructibility result for Shelah cardinals."}]