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set_universe [2015/08/25 22:49]
nikolaj
set_universe [2015/08/25 22:49] (current)
nikolaj
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 In [[set theory]], the Tarski axiom states that there is a Grothendieck universe for every set. Note that this axiom implies the existence of strongly inaccessible cardinals and goes beyond ZFC. In [[set theory]], the Tarski axiom states that there is a Grothendieck universe for every set. Note that this axiom implies the existence of strongly inaccessible cardinals and goes beyond ZFC.
  
-=== Predicates === +== Motivation ==
-| @#EEEE55: predicate | @#EEEE55: $X$... small set $\equiv X\in{\mathfrak U}_\mathrm{Sets}$ | +
- +
-=== Motivation ​===+
 When one writes down a proposition in set theory, e.g.  When one writes down a proposition in set theory, e.g. 
  
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   * Shielding from the famous set theoretical paradoxes   * Shielding from the famous set theoretical paradoxes
   * ${\mathfrak U}_\mathrm{Sets}$ in the object language, which easily lets one define a category of sets, [[Set]].   * ${\mathfrak U}_\mathrm{Sets}$ in the object language, which easily lets one define a category of sets, [[Set]].
 +
 +=== Predicates ===
 +| @#EEEE55: predicate | @#EEEE55: $X$... small set $\equiv X\in{\mathfrak U}_\mathrm{Sets}$ |
  
 ----- -----
 === Requirements === === Requirements ===
 [[Grothendieck universe]], [[First infinite von Neumann ordinal]] [[Grothendieck universe]], [[First infinite von Neumann ordinal]]
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