User blog:Maxywaxy/Do any functions reach this growth rate?

Four questions: Thanks
 * 1) Are any functions are known to be approximately or stronger than \(f_{\Gamma_{0}}(n)\)?
 * 2) What's the fastest growing unary function with a known growth rate?
 * 3) What's the fastest growing function with a known growth rate?
 * 4) What's the fastest growing function known and understood?