# Godel: are all undecidable props in consistent math systems subsets of self-referent statements? **URL:** \ **Category:** Factual Questions\ **Created:** [December 9, 2009, 4:02am UTC](https://boards.straightdope.com/t/godel-are-all-undecidable-props-in-consistent-math-systems-subsets-of-self-referent-statements/520559 "2009-12-09T04:02:12Z")\ **Posts on this page:** 1\ **Showing post:** 104
**Author:** ![ch4rl3s](https://avatars.discourse-cdn.com/v4/letter/c/c4cdca/32.png) [@ch4rl3s](https://boards.straightdope.com/u/ch4rl3s)\ **Post date:** [December 15, 2009, 4:30pm UTC](https://boards.straightdope.com/t/godel-are-all-undecidable-props-in-consistent-math-systems-subsets-of-self-referent-statements/520559/104 "2009-12-15T16:30:26Z")
> [@Frylock](#): > > You don’t understand what the wiki says. That they are a “theory of the natural numbers with addition” doesn’t mean that they can apply only to the natural numbers, and certainly doesn’t mean that they can apply only to the natural numbers even when embedded in an extension. You finally admit that Presburger, P, is at once a complete system and has extensions where the truth value of a question appears to be different? I’ve finally realized that Presburger asks the question, “is there an x in the natural numbers such that x+x=3?” has the same value in every extension of P. [QUOTE=Capt. Ridley’s Shooting Party] you seem to recognize that fields other than F2 exist, yet are convinced that the field axioms only describe F2 [/QUOTE] Everyone else seems to deny that the field axioms describe F2. But, what I actually am convinced of is “the field axioms only, … describe F2.” the field axioms without any other axioms, creates a perfectly valid system of their own. F is the smallest system that satisfies the axioms of F; and not coincidentally, they describe the smallest possible field. Everyone else has been seeming to deny that. Even though it should be obvious that that can and should be true. And if Frylock continues to believe that Presburger assures us that x+x=3 is false for every domain we extend Presburger to, he’s going to have to keep denying that we can create an extension where 1.5 is a number. And that would tend to make him irrelevant for any further advancement of this thread, or my own knowledge. Capt. Ridley, I think, started irrelevant for my purposes. > [@](#): > > You haven’t supplied a single truth table in this thread Are you complaining that I don’t know how to embed an actual table in this thread, and instead, spelled out the value for every set of elements? Or, that I used the wrong term. I don’t know, you haven’t said. So, you’re not even trying to help. I am teachable if I get the proper information. Even when it comes from people, (like Frylock,) who don’t know what it means themselves, and I have to come up with the answers myself. --- _[View the full topic](https://boards.straightdope.com/t/godel-are-all-undecidable-props-in-consistent-math-systems-subsets-of-self-referent-statements/520559)._