Skip to main content
MathOverflow

You are not logged in. Your edit will be placed in a queue until it is peer reviewed.

We welcome edits that make the post easier to understand and more valuable for readers. Because community members review edits, please try to make the post substantially better than how you found it, for example, by fixing grammar or adding additional resources and hyperlinks.

11
  • 9
    $\begingroup$ Thank you. All this evidence is not a joke for me. By now I believe the founding of diagonal argumentation is tantamount to the the founding of the group concept. $\endgroup$ Commented Nov 22, 2010 at 18:53
  • 13
    $\begingroup$ A lot of these can be captured by Lawvere's formalisation of the diagonal argument as a fixed-point theorem: tac.mta.ca/tac/reprints/articles/15/tr15abs.html $\endgroup$ Commented Nov 22, 2010 at 22:47
  • 12
    $\begingroup$ David, I agree, but another perspective is simply that the fixed-point theorem is another instance of diagonalization. That is, these arguments are already unified as diagonalizations. $\endgroup$ Commented Nov 22, 2010 at 23:30
  • 9
    $\begingroup$ Joel - I agree that calling them diagonalisation arguments or fixed point theorems is just a point of linguistics (actually the diagonal argument is the contrapositive of the fixed point version), it's just that Lawvere's version, to me at least, looks more like a single theorem than a collection of results that rely on an particular line of reasoning. This, I hope, helps the OP or those answering the question in isolating what a diagonal argument "is", and avoid it if possible. $\endgroup$ Commented Nov 23, 2010 at 4:54
  • 8
    $\begingroup$ The existence of forcing extensions is also an application of diagonalization. $\endgroup$ Commented Sep 7, 2017 at 6:28