Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The finite spectrum of a first-order sentence is the set of positive integers that are the sizes of its models. The class of finite spectra is known to be the same as the complexity class NE.  consider the spectra obtained by limiting models to be either planar (in the graph-theoretic sense) or by bounding the degree of elements.  show that the class of such spectra is still suprisingly rich by establishing that significant fragments of NE are included among them. At the same time,  establish non-trivial upper bounds showing that not all sets in NE are obtained as planar or bounded-degree spectra.
['Anuj Dawar', 'Eryk Kopczyński']
I am writing a research paper on a idea Bounded degree and planar spectra
[{"from": "human", "value": "I am writing a research paper on a idea Bounded degree and planar spectra"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The finite spectrum of a first-order sentence is the set of positive integers that are the sizes of its models. The class of finite spectra is known to be the same as the complexity class NE.  consider the spectra obtained by limiting models to be either planar (in the graph-theoretic sense) or by bounding the degree of elements.  show that the class of such spectra is still suprisingly rich by establishing that significant fragments of NE are included among them. At the same time,  establish non-trivial upper bounds showing that not all sets in NE are obtained as planar or bounded-degree spectra."}]