Question about universal set

On Mon, 27 Feb 2006, Dave Seaman wrote:
Others have answered this, but I would like to point out that there is
another way to prove the nonexistence of the universal set that doesn't
use the axiom of separation. The idea is based on Cantor's Paradox.

Suppose a universal set U exists. Let P(U) be its power set. By
Cantor's theorem, there must exist an x in P(U) that is not in U,
contrary to the assumption that U is a universal set.

Ouch. Here's simplest proof. Assume
(Ax) x in u
Then
u in u
contradicts regularity.

.

Relevant Pages

  • Re: Question about universal set
    ... Separation overcomes the problem of contradiction first pointed out by ... 2.- Ez Ay or, in other words z is the universal set. ... its negation of the Axiom of Separation? ... When people say that the axiom of separation overcomes Cantor's paradox, ...
    (sci.math)
  • Re: Question about universal set
    ... Separation overcomes the problem of contradiction first pointed out by ... So the axiom is contradicted if either ... If the universal set existed, Russell's set would exist by the ... and that would lead to contradiction. ...
    (sci.math)
  • Re: Question about universal set
    ... Suppose a universal set U exists. ... contradicts regularity. ... I guess the Axiom of Separation is still ...
    (sci.math)
  • Re: Question about universal set
    ... use the axiom of separation. ... The idea is based on Cantor's Paradox. ... Suppose a universal set U exists. ... contradicts regularity. ...
    (sci.math)
  • Type Theory TT Corrected.
    ... Completeness axiom for V: ... Axiom schema of restricted Stratified Comprehension: ... non universal set is universal set since it is in itself. ... that are not ordinals, etc...... ...
    (sci.logic)
Quantcast