User blog:Ynought/Another question

I had an idea for a function that possibly outgrows \(f_{\text{PTO}(\text{ZFC})}(n)\) but if there exists an formal theory,lets call it \(\text{L}\),such that \(\text{PTO}(L)\geq \omega_1^{\text{CK}}\).Because if such an theory does exist then the function could be the either the fastest growing computable or one of the fastest growing uncomputable ones.Thanks for your help.