No, a stock split does not increase your wealth; you merely receive more stock certificates evidencing the same ownership interest in the company that issued the stock.
Your overall cost basis is not changed as a result of a stock split, but your per share basis is changed.
You will need to adjust your basis per share of the stock. If you realize a gain when you sell the stock, you will have to include the gain in income. Gain is the amount by which the proceeds from the sale, minus sales commissions, exceed the adjusted basis of the stock sold.