Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Suppose that λ=λ  λ++. In fact,  work more generally with abstract elementary classes. The criterion for the consistent existence of universals applies to various ll known theories, such as triangle-free graphs and simple theories. Having in mind possible applications in analysis,  further observe that for such λ, for any fixed μ>λ+ regular with μ=μλ+, it is consistent that 2λ=μ and there is no normed vector space over ℚ of size <μ which is universal for normed vector spaces over ℚ of dimension λ+ under the notion of embedding h which specifies (a,b) such that ||h(x)/||x∈(a,b) for all x.
['Mirna Džamonja', 'Saharon Shelah']
I am writing a research paper on a idea On the existence of universal models
[{"from": "human", "value": "I am writing a research paper on a idea On the existence of universal models"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Suppose that \u03bb=\u03bb  \u03bb++. In fact,  work more generally with abstract elementary classes. The criterion for the consistent existence of universals applies to various ll known theories, such as triangle-free graphs and simple theories. Having in mind possible applications in analysis,  further observe that for such \u03bb, for any fixed \u03bc>\u03bb+ regular with \u03bc=\u03bc\u03bb+, it is consistent that 2\u03bb=\u03bc and there is no normed vector space over \u211a of size <\u03bc which is universal for normed vector spaces over \u211a of dimension \u03bb+ under the notion of embedding h which specifies (a,b) such that ||h(x)/||x\u2208(a,b) for all x."}]