Take a look on the bottom or back of your radio. You should see something about FCC rules Part 15:
This device must accept any interference received, including interference that may caused undesired operation.
Unfortunately, your neighbor's shredder is most likely an unshielded motor with a gearbox and a perfect example of a wide-band RF noise generator. It basically spews electromagnetic interference (EMI) when it's on. The reason that is allowed is because it is fairly limited in power and range; it's not a transmitter. You just have the unlucky circumstance of having your receiver near it.
There are a few things you might do:
- Chat with your neighbor about moving it to a different location in her apartment. It may be that simply moving it helps.
- Consider moving your receiver; for the same reasons as above, putting some distance between it and the shredder may help enough.
- Extend the antenna location with a shielded coaxial cable. You may be able to move the antenna to a location or position that is away from the shredder or oriented to reject noise from it, while leaving the radio in the desired location.
- In theory if your neighbor was very concerned, she could wrap the shredder (at least partly) in shielding and ground it to attenuate a lot of the noise. However, it would be ugly and inconvenient, so don't hold out for this solution.
I almost forgot to address the shared electrical power issue. The shredder can also inject noise back to the circuit from which it's powered. In that case, if you share an electrical circuit (or even if it's not shared, but your two circuits are short distances away from a common breaker panel) the noise could be originating from power instead of exclusively being picked up in air. Some things to try:
Move the radio to a different outlet, hopefully on a different circuit. Depending on the size of your apartments, this may or may not make a difference.
Add a filter (ferrite bead) to the power cord, to help remove higher-frequency noise.
Power the radio from a battery or uninterruptible power supply that is disconnected from the apartment circuit. (As Andy suggested in comments.)
If you are able to identify that the bulk of the noise/interference is coming from a shared electrical connection, you may be able to take more steps to isolating it. But those are my most immediate suggestions.