Could people become immune to radiation if we have been exposed to the small amount of it?

Could people become immune to radiation if we have been exposed to the small amount of it?
Coming from the Post-Soviet Union country it was common for young soldiers to go to secret missions and protect the radioactive places with code names.

Many people had to serve at Chernobyl, my 18 years old grandpa served at City 40 along with other young soldiers from the Soviet Union, in 1957, and while he was not affected and lived to 82, and we are all perfectly healthy as well, he was still exposed to the small dosage of it.

I wonder if it is possible to have the immunity to the light radiation if your ancestor was exposed to it.
Updates
+1 y
*resistant I mean :P
Could people become immune to radiation if we have been exposed to the small amount of it?
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