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Results tagged with lo.logic
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user 461
first-order and higher-order logic, model theory, set theory, proof theory, computability theory, formal languages, definability, interplay of syntax and semantics, constructive logic, intuitionism, philosophical logic, modal logic, completeness, Gödel incompleteness, decidability, undecidability, theories of truth, truth revision, consistency.
100
votes
16
answers
29k
views
What if Current Foundations of Mathematics are Inconsistent? [closed]
The title of the question is also the title of a talk by Vladimir Voevodsky, available here.
Had this kind of opinion been expressed before?
EDIT. Thanks to all answerers, commentators, voters, an …
6
votes
0
answers
198
views
Isomorphism of hyperreal fields viewed as extensions of the field of reals
I asked this question on Mathematics Stackexchange but got no answer.
Question. Does $ZFC$ prove that there are non-principal ultrafilters $\mathcal U$ and $\mathcal V$ over $\mathbb N$ such that the …
- 4,416
4
votes
Is PA consistent? do we know it?
Here are four quotes:
Quote 1. Vladimir Voevodsky
"To put it very shortly I think that inconsistency of Peano arithmetic as well as inconsistency of ZFC are open and very interesting problems in mat …
2
votes
What does it mean for a mathematical statement to be true?
In my humble opinion, the best reference for this kind of questions is Bourbaki's "Set Theory" ... Actually, I would recommend Bourbaki's book to people who, like me, have trouble to understand other …
1
vote
How would one even begin to try to prove that a simple number-theoretic statement is undecid...
EDIT
Here is my problem. To prove that statement S is undecidable is to
(1) prove that one cannot prove S.
I think I understand the meaning of the second "prove". (It depends of course on the cont …
- 4,416