[pliny]

The price of the share stays the same but there are fewer shares, so the market cap would go down.

[mrkstu]

But EPS rises so equilibrium would suggest the price of the share would almost certainly rise to match the old EPS.

[fiprofessor]

The earnings per share certainly increases. But this is (at least theoretically) offset by the fact that the firm's assets have decreased. For example, if the buyback was paid for with cash, then prior to the buyback, the shares represented a claim of ownership not just on future earnings, but also on that cash reserve.

That said, this is all under a theoretical model (as in Miller-Modigliani theorem). In practice/empirically, there is reason to plausibly believe that e.g. the decision to announce a buyback has a signalling effect and so can increase share prices.

[User23]

This isn’t even necessarily true for dividend yield let alone for EPS.