User blog comment:O0112111/How do indescribables work?/@comment-35470197-20190907214605/@comment-35470197-20190908093023

Since you caught a wrong definition, it does not work. Well, the word "work" is ambiguous for you. Since you originally wrote "how is the structure \((V_{\kappa+n},\in,A)\) defined", I guess that your "work" means "determined" or something like that. First of all, \(n\) is given (since you did not use \(n\) in the condition of \(\varphi\), your definition is wrong.). Moreover, \(A\) is universally quantified. Therefore you do not have to define, determine, or characterise from \(\kappa\). So the problem seems not to be the understanding of the large cardinal axiom, but the understanding of general conventions of first order logic such as quantifiers, defining formulae, satisfaction, and so on. Then it is good to start with study of basic set theory.