A Relatively Small Turing Machine Whose Behavior Is Independent of Set Theory · HackerPapers discussions

A Relatively Small Turing Machine Whose Behavior Is Independent of Set Theory — mentioned by renewiltord

Sat, 28 Jun 2025 20:07:44 GMT

I don’t get it. What’s wrong with the post? And https://arxiv.org/abs/1605.04343 is interesting, no?

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A Relatively Small Turing Machine Whose Behavior Is Independent of Set Theory — mentioned by bubblyworld

Thu, 29 May 2025 06:52:11 GMT

I don't think this is an important distinction. The point of Turing machines is that you can ask questions like "can all instances of this problem be solved uniformly, and how relatively expensive is it?". This requires infinite memory in a formal sense, because instances of (most) problems can be arbitrarily large. Yes, if you ask the same question with a fixed (finite) memory restriction on everything, the answer is uninteresting. To me, this is... uninteresting. It tells you nothing about the underlying logical structure of your problem, which is what mathematicians are really trying to…

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A Relatively Small Turing Machine Whose Behavior Is Independent of Set Theory — mentioned by ttctciyf

Wed, 28 May 2025 23:26:49 GMT

> Are these two meanings of "undecidable" related I can't claim to answer this, but you might like to look at A Relatively Small Turing Machine Whose Behavior Is Independent of Set Theory[0] which (amongst other interesting things) does discuss the proposition "ZFC is consistent", which is independent from ZFC, in terms of a Turing Machine which enumerates all possible proofs in ZFC and halts when it finds a contradiction (e.g. a proof of 0=1). But I don't think there's a simple equivalence here, all the same. The logician's undecidable is always relative to a set of axioms, whereas the…

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A Relatively Small Turing Machine Whose Behavior Is Independent of Set Theory — mentioned by sp332

Mon, 10 Jul 2023 01:01:30 GMT

There's a lot of introduction here, but it starts getting to the point in section 3.4 "The previous paper". That paper is "A Relatively Small Turing Machine Whose Behavior Is Independent of Set Theory" https://arxiv.org/abs/1605.04343 (and an improvement in the blog comments on https://scottaaronson.blog/?p=2725) I recommend starting there just to know where the conversation is going and then coming back to this.

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