Skip to main content
MathOverflow

Return to Question

Changed the font type of the set theories names
Source Link
Noah Laikin
Noah Laikin
  • 53
  • 5

In Shulman's 2008 paper 'Set Theory for Category Theory', he includes amongst the axioms of NBG$\sf NBG$ the axiom of limitation of size. Being well known to imply the axiom of global choice, it seems to me that since ZFC+I$\sf ZFC+I$ doesn't imply global choice, this should be inconsistent with his later remark that ZFC+I$\sf ZFC+I$ has a model of NBG$\sf NBG$ given by $V_{\kappa}$ for the sets, and $\operatorname{Def}(V_{\kappa})$ for the proper classes. I'm sure there is something here I don't quite understand, I would greatly appreciate some clarification.

In Shulman's 2008 paper 'Set Theory for Category Theory', he includes amongst the axioms of NBG the axiom of limitation of size. Being well known to imply the axiom of global choice, it seems to me that since ZFC+I doesn't imply global choice, this should be inconsistent with his later remark that ZFC+I has a model of NBG given by $V_{\kappa}$ for the sets, and $\operatorname{Def}(V_{\kappa})$ for the proper classes. I'm sure there is something here I don't quite understand, I would greatly appreciate some clarification.

In Shulman's 2008 paper 'Set Theory for Category Theory', he includes amongst the axioms of $\sf NBG$ the axiom of limitation of size. Being well known to imply the axiom of global choice, it seems to me that since $\sf ZFC+I$ doesn't imply global choice, this should be inconsistent with his later remark that $\sf ZFC+I$ has a model of $\sf NBG$ given by $V_{\kappa}$ for the sets, and $\operatorname{Def}(V_{\kappa})$ for the proper classes. I'm sure there is something here I don't quite understand, I would greatly appreciate some clarification.

Schulman -> Shulman; link to article
Source Link
LSpice
LSpice
  • 12.9k
  • 4
  • 45
  • 69

In Schulman'sShulman's 2008 paper 'Set Theory for Category Theory''Set Theory for Category Theory', he includes amongst the axioms of NBG the axiom of limitation of size. Being well known to imply the axiom of global choice, it seems to me that since ZFC+I doesn't imply global choice, this should be inconsistent with his later remark that ZFC+I has a model of NBG given by $V_{\kappa}$ for the sets, and Def$\hspace{0.1em}(V_{\kappa})$$\operatorname{Def}(V_{\kappa})$ for the proper classes. I'm sure there is something here I don't quite understand, I would greatly appreciate some clarification.

In Schulman's 2008 paper 'Set Theory for Category Theory', he includes amongst the axioms of NBG the axiom of limitation of size. Being well known to imply the axiom of global choice, it seems to me that since ZFC+I doesn't imply global choice, this should be inconsistent with his later remark that ZFC+I has a model of NBG given by $V_{\kappa}$ for the sets, and Def$\hspace{0.1em}(V_{\kappa})$ for the proper classes. I'm sure there is something here I don't quite understand, I would greatly appreciate some clarification.

In Shulman's 2008 paper 'Set Theory for Category Theory', he includes amongst the axioms of NBG the axiom of limitation of size. Being well known to imply the axiom of global choice, it seems to me that since ZFC+I doesn't imply global choice, this should be inconsistent with his later remark that ZFC+I has a model of NBG given by $V_{\kappa}$ for the sets, and $\operatorname{Def}(V_{\kappa})$ for the proper classes. I'm sure there is something here I don't quite understand, I would greatly appreciate some clarification.

Became Hot Network Question
Source Link
Noah Laikin
Noah Laikin
  • 53
  • 5

NBG, ZFC+I, and Global Choice

In Schulman's 2008 paper 'Set Theory for Category Theory', he includes amongst the axioms of NBG the axiom of limitation of size. Being well known to imply the axiom of global choice, it seems to me that since ZFC+I doesn't imply global choice, this should be inconsistent with his later remark that ZFC+I has a model of NBG given by $V_{\kappa}$ for the sets, and Def$\hspace{0.1em}(V_{\kappa})$ for the proper classes. I'm sure there is something here I don't quite understand, I would greatly appreciate some clarification.