> expressive enough to produce
you understand that "expressive enough to produce" are not obvious elements of zfc, that's some average consumer napkin math and not strict formalization.
> expressive enough to produce
you understand that "expressive enough to produce" are not obvious elements of zfc, that's some average consumer napkin math and not strict formalization.
why should they be obvious? they are derived and have been thoroughly proven.
looks like we are in disagreement
A quick google search shows different proof assistants have been used to obtain the Peano axioms from ZFC, such as Isabelle/ZF and Metamath. I think you're just wrong
What are you nerds fighting about please explain
you are entitled to have your opinion :-)
and you are entitled to talk about maths while rejecting maths
coming back to your argument about peano being obtained from zfc, you obviously can't prove that it happened using purely zfc, and not some logical framework embedded into those proof assistants.
I said I am not expert, I am indeed not expert in zfc and godel theorems, but I am an expert (phd) in actual formalization theory. Formal theory is very simple concept: its alphabet, set of formulas on top of this alphabet, and function which translates one formula to another.
ZFC can't "obtain" peano, simply because it doesn't have say * operator defined. You need to do something on top of it. Additionally, zfc itself looks like loosely formalized say in wikipedia (and I am not sure if there is any strict formalization anywhere), we take it as common sense that it can utilize some simple logical rules (e.g. modus ponens), but what are exactly rules, which could be separate topic of research, this detail is skipped.
That increases the likelihood that they are right.
> support your point with explanation or be ignored :-)
Anyone who says "Godel theorems are for systems with basic arithmetic, zfc doesn't include arithmetic, thus are not object of Godel theorems" and isn't joking warrants a permanent ignore.
https://math.stackexchange.com/questions/1366560/why-does-g%...
https://math.stackexchange.com/questions/1090437/how-to-prov...
imo, those two links are example of rather low quality weird math discussions, but you can keep your opinion