I read that Presburger arithmetic is decidable while Peano arithmetic is undecidable, and actually Peano arithmaetic extends Presburger arithmetic just with the addition of the multiplication operator. Can someone please give me the 'intutive' idea behind this?
Or probably a formula in Peano arithmetic that cannot be proved. Does it have something to do with the self reference paradox in Goedel's Incompleteness Theorem?
Regards