Why? I know certain people (i.e. Chaitin, who’s a bit cranky in this regard) have toyed around with the idea, but is there any reason to believe it?
Not any strong one. We do know that some systems similar to the integers have their analogs to be false, but for most analogs (such as the finite field case) it seems to be true. That’s very weak evidence for undecidability. However, I was thinking more in contrast to something like the classification of finite simple groups as of 1975 where there was a general program of what to do that had no obvious massive obstructions.
Not any strong one. We do know that some systems similar to the integers have their analogs to be false, but for most analogs (such as the finite field case) it seems to be true. That’s very weak evidence for undecidability. However, I was thinking more in contrast to something like the classification of finite simple groups as of 1975 where there was a general program of what to do that had no obvious massive obstructions.