1

Apologies in advance for what is most likely an incredibly naive question. I know absolutely nothing about category theory; this theorem is what led me to my first true exposure to it.

I have an intuitive sense that things like Tarski's Undecidability Theorem and Godel's Incompleteness Theorems can be "generalized", but what formal implications does this generalization entail? Does this theorem entail, for instance that these ultimately converge on a similar conclusion, or that they can be equivalated in certain contexts?

Jay
  • 39
  • 2
    See Yanofsky: https://arxiv.org/abs/math/0305282 – Qiaochu Yuan Jan 06 '25 at 23:16
  • Related question: https://math.stackexchange.com/questions/3540445/can-russells-paradox-halting-problem-and-godels-incompleteness-theorem-be-gen/ (with some further links, including the paper linked by Qiaochu Yuan) – Mark Kamsma Jan 07 '25 at 11:21
  • Thank you both. – Jay Jan 07 '25 at 18:34
  • 1
    My memory is a bit hazy because it's a while since I looked into it / thought about it, but I believe it's a generalisation in the sense that the other theorems are a special case of it. For example, you might think intuitively that the Halting problem and Gödel's incompleteness theorem are kind of similar, with similar kinds of proof. Then Lawvere's fixed point theorem tells you that's not a coincidence because they're actually two instances of the same thing. – N. Virgo Jan 08 '25 at 00:36
  • @Jay: Actually, there is not much benefit in such generalizations because it's like saying both "duck" and "magnificent adult baby" can be generalized to "animal". – user21820 Feb 08 '25 at 03:14

0 Answers0