Precise temperature reading on induction cooker
I use a Sunartis E514 digital household thermometer on an induction stove, and I get normal readings. 

I can't say it is the best thermometer out there, as it is a bit slow. The specification is 4 to 10 seconds measuring time. From experience, it doesn't need 4 seconds to change the display when immersed in hot liquid, but while it gives you the temperature with 0.1°C precision, I guess this temp is slightly lagging. That can ruin a batch of candy or dark chocolate, but these are still doable if you are mentally accounting for the lag. It is great for everything else. The low price is another advantage. 

I can't promise 100% that it will work with any induction stove. Mine is a small portable one, and maybe its magnetic field is weaker than that of a full-sized stove. For temperature-sensitive applications, I usually cook on 500 Watt, but I've had the thermometer inside (also very close to the bottom of the pot) at higher settings, so I hope it will work. Nevertheless, it is probably a good idea to get it from a place with good return policy.