Tagged Questions
2
votes
1answer
140 views
A qualitative, yet precise statement of Godel's incompleteness theorem?
I read online a statement to the effect that (I'm paraphrasing):
Goedel's incompleteness theorem shows that we cannot even have a complete and consistent theory for the natural numbers.
I am ...
4
votes
0answers
119 views
Freeman Dyson's example of an unproveable truth
Freeman Dyson has claimed that
$\not \exists m,n Reversed(2^n) = m ^ 5 $
(where Reversed(l) just is the reverse of the digits of l in base 10), is probably an example of an unproveable truth ...
3
votes
0answers
124 views
Is there any recursive definition, using only addition, of the set of values of $x^2+y^2$?
There is a recursive definition of the set of squares which uses only addition:
$CS(x,y) := IS(x) \wedge IS(y) \wedge x \lt y \wedge \forall z: (x
\lt z) \wedge (z \lt y)⇒\neg IS(z)$
$IS(x)⇔ x=0 ...
11
votes
1answer
342 views
What's the theory in which incompleteness of PA is proved?
Maybe this is a dumb question, but I have to admit that it is not really clear to me what the theory is, in which incompleteness of PA and stronger theories is proved. The texts I did study so far are ...
