Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study Vaught's problem for quite o-minimal theories. Quite o-minimal theories form a subclass of the class of akly o-minimal theories preserving a series of properties of o-minimal theories.  investigate quite o-minimal theories having fer than   2 ω        2    ω          countable models and prove that the Exchange Principle for algebraic closure holds in any model of such a theory and also  prove binarity of these theories. The main result of the paper is that any quite o-minimal theory has either   2 ω        2    ω          countable models or   6 a 3 b        6    a      3    b          countable models, where  a  and  b  are natural numbers.
['B. Sh. Kulpeshov', 'S. V. Sudoplatov']
I am writing a research paper on a idea Vaught's conjecture for quite o-minimal theories
[{"from": "human", "value": "I am writing a research paper on a idea Vaught's conjecture for quite o-minimal theories"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study Vaught's problem for quite o-minimal theories. Quite o-minimal theories form a subclass of the class of akly o-minimal theories preserving a series of properties of o-minimal theories.  investigate quite o-minimal theories having fer than   2 \u03c9        2    \u03c9          countable models and prove that the Exchange Principle for algebraic closure holds in any model of such a theory and also  prove binarity of these theories. The main result of the paper is that any quite o-minimal theory has either   2 \u03c9        2    \u03c9          countable models or   6 a 3 b        6    a      3    b          countable models, where  a  and  b  are natural numbers."}]