The Fundamental Theorem of Asset Pricing (FTAP) in mathematical finance also comes in two parts. The first part says, more or less, that a market is arbitrage-free if and only if there is an equivalent martingale measure for the discounted price process. The second part says that the market is complete (all European options can be hedged) if and only if the equivalent martingale measure is unique.
(In some models, you may need an appropriate definition of "arbitrage-free", such as the notion of "no free lunch with vanishing risk", and you may replace "equivalent martingale measure" with "equivalent local martingale measure". But the idea is the same.)