XPost: sci.math, sci.physics.relativity   
   From: janburse@fastmail.fm   
      
   Hi,   
      
   You should read more books about set theory.   
   You get that a classes are in general not   
   sets from the unrestricted comprehension axiom alone:   
      
   "Because restricting comprehension avoided   
   Russell's paradox, several mathematicians   
   including Zermelo, Fraenkel, and Gödel considered   
   it the most important axiom of set theory   
   https://en.wikipedia.org/wiki/Axiom_schema_of_specification   
      
   Its totally independent from axion of   
   choice, or well founded axioms. Just study   
   the usual paradox in the Russell set,   
      
   works always! Whats unrestricted comprehension.   
   Well if V, the class of all sets would be a set,   
   you could use it in restricted comprehension:   
      
   y = { x e V | P(x) }   
      
   Now use as P(x) <=> ~x e x and substitute y for x.   
   You get this contradiction:   
      
   Case 1: If y e y then P(y), then ~y e y.   
   Case 2: if ~y e y then ~P(y), then y e y.   
      
   Nice circularity over a negation hop, y e y <-> ~y e y.   
      
   Ross Finlayson schrieb:   
   > I never even heard of ZF until the late '90's.   
   > I wonder why a class is not a set. In foundational logic, a class is not   
   > a set. That is talk about ZF with the anti-foundation axiom."   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)