Tagged Questions
1
vote
1answer
56 views
What percentage of formulas is unprovable in a given axiomatic system?
I am trying to use language I am not familiar with, so bear with me. If I make no sense, I try to be clearer.
Assume we are given a formal language. Assume $S$ is the set of every well-formed formula ...
3
votes
1answer
110 views
System with infinite number of axioms
Assume we have a set of axioms $A_0$. There exists a statement that can be formulated with these axioms that cannot be proven to be true with this system. Assume we give such a statement axiomatic ...
2
votes
2answers
701 views
Is Gödel's theorem invalid? [closed]
Right now I've skim through Gödel's theorem is invalid by Diego Saá on arXiv (freely available).
As it seems very plausible, I ask for any references and scrutinizations of the paper.
8
votes
2answers
180 views
Axiomatic system and Hilbert's 2nd problem
Hilbert's second problem asks if the axioms of arithmetic are consistent. Has this problem been resolved? Shouldn't an axiomatic system ideally be consistent and complete(given that we have the ...
0
votes
1answer
130 views
Consistent but incomplete formal axiomatic systems
Is there any known consistent but incomplete formal axiomatic system apart of and simpler than one "capable of doing arithmetic"? Is it even possible?
Even if this capability of arithmetic were a ...
5
votes
2answers
197 views
“Completeness modulo Godel sentences”?
So this has been bugging me for roughly four years. When I was an undergraduate, I attended a colloquium in which the speaker was a 'cheerleader' for AD (the axiom of determinacy- an alternative to ...
