« first day (888 days earlier)      last day (2224 days later) » 

famesyasd
famesyasd
01:57
I was reading about Godel's Incompleteness theorem's and on this part my brain melted. Could someone please elaborate this?
"Gödel’s completeness theorem implies that a statement is provable using a set of axioms if and only if that statement is true, for every model of the set of axioms. That means that for any unprovable statement, there has to be a model of those axioms for which the statement is false.
But, if the consistency of the set of axioms is unprovable, that means there has to be a model of your axioms where the consistency statement is false."
Malice Vidrine
Malice Vidrine
02:20
@user21820 Can explain this better than me, but the outline is this. Con(T) is (generally) the statement that no proof exists of a contradiction, but a "proof" in this case is a particular natural number with certain arithmetic properties. A model in which -Con(T) holds is one in which the model's natural numbers have non-standard numbers that allow the "proof of contradiction" to exist.
In other words, the model is using a really weird notion of "proof".

« first day (888 days earlier)      last day (2224 days later) »