Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  prove that if G is a group definable in a saturated o-minimal structure, then G has no infinite descending chain of type-definable subgroups of bounded index. Equivalently, G has a smallest (necessarily normal) type-definable subgroup G 00 of bounded index and G/G 00 equipped with the “logic topology” is a compact Lie group. These results give partial ansrs to some conjectures of the fourth author.
['Alessandro Berarducci', 'Margarita Otero', 'Yaa’cov Peterzil', 'Anand Pillay']
I am writing a research paper on a idea A descending chain condition for groups definable in o-minimal structures
[{"from": "human", "value": "I am writing a research paper on a idea A descending chain condition for groups definable in o-minimal structures"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  prove that if G is a group definable in a saturated o-minimal structure, then G has no infinite descending chain of type-definable subgroups of bounded index. Equivalently, G has a smallest (necessarily normal) type-definable subgroup G 00 of bounded index and G/G 00 equipped with the \u201clogic topology\u201d is a compact Lie group. These results give partial ansrs to some conjectures of the fourth author."}]