How does share buybacks affect the different ratios and the stock price?

So if i understand correctly when a company buys back shares it basically gets wiped from the system so there will be less shares for the same holders which means higher stock price, higher EPS, higher P/E, etc without the fundamentals changing.

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So a rough example in an ideal environment: if apple has a 15P/E and gets the same exact results in 2 years and announces a 50% share buyback the stock price doubles but since the revenue/profits did not increase the P/E doubles as well.

Is this correct or am i missing something? So basically high P/E doesnt mean anything as long as the company buys back shares.