$$T=\{\langle M\rangle \mid |L(M)| =1 \text{ or } |L(M)| >2\}$$I started with Rice's theorem (come up with an example where $|L(M)| = 2$) to see that $T$ was undecidable. Then I figured out $\bar{T}$ was unrecognizable, because $H =\{\langle M \rangle \mid M\text{ halts on the empty string} \}$ has a mapping-reduction to $T$, and $H$ is not co-recognizable, so $T$ is not co-recognizable.Now I'm stuck. I tried mapping-reductions from $H$, $E = \{\langle M \rangle \mid M \text{ doesn't accept anything} \}$ and $F = \{ \langle M \rangle \mid L(M) \text{ is finite} \}$.What's a good set to try and reduce from (or reduce to)? Am I right that $T$ is unrecognizable?
Is $T=\{\langle M\rangle \mid |L(M)| =1 \text{ or } |L(M)| >2\}$ recognizable?
computability;turing machines;semi decidability