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Three facts:

(1)The constructible universe L is the minimal model for ZFC;

(2) L is a model of "there exists an inaccessible cardinal [tex]\kappa[/tex]"; and

(3) if V=L, an inaccessible cardinal [tex]\kappa[/tex] with the membership relation [tex]\epsilon[/tex] is a model of ZFC.

So, what is confusing me is: if the universe of L contains[tex]\kappa[/tex] [tex]^{L}[/tex] , then how can L be the minimal model? Wouldn't <[tex]\kappa[/tex],[tex]\epsilon[/tex]>" be a model that is smaller?

P.S. Why are my Greek letters all getting superscripted? I only asked for L in (3) to be superscripted.

(1)The constructible universe L is the minimal model for ZFC;

(2) L is a model of "there exists an inaccessible cardinal [tex]\kappa[/tex]"; and

(3) if V=L, an inaccessible cardinal [tex]\kappa[/tex] with the membership relation [tex]\epsilon[/tex] is a model of ZFC.

So, what is confusing me is: if the universe of L contains[tex]\kappa[/tex] [tex]^{L}[/tex] , then how can L be the minimal model? Wouldn't <[tex]\kappa[/tex],[tex]\epsilon[/tex]>" be a model that is smaller?

P.S. Why are my Greek letters all getting superscripted? I only asked for L in (3) to be superscripted.

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