Let introduce the "Exactly $\{m_{1},m_{2}\}$-SAT" problem : Given a CNF formula $F$ and $2$ integers $m_{1}$ and $m_{2}$, is it true that $F$ has exactly $m_{1}$ or $m_{2}$ models ?
I guess Exactly $\{m_{1},m_{2}\}$-SAT ($m_{1}\leq m_{2}$) is many-one polynomial time reducible to the parametrized problem "Exactly $m_2$-SAT" with $m_2$ considered as a parameter : Given a CNF formula $F$ is it true that $F$ has exactly $m_{2}$ models.
Is it correct ?
Thank you for your answer.