Newton-Cartan theory formalizes this: the degenerate metric structure of Galilean spacetime selects inertial frames without invoking additional geometric fields beyond the topology.

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Degenerate metric(as used in mathematics and physics): A mathematical tool for measuring distances and relationships in space that breaks down or loses information in a specific way, unlike normal metrics that work uniformly everywhere.
Galilean spacetime(as used in physics and philosophy of time): The classical view of space and time from the 1600s (before Einstein), which treats space and time as completely separate things.
Inertial frames(as a concept from physics that describes how motion is measured): Imaginary reference points or perspectives from which you measure motion and position; think of them as different viewpoints from which an observer could describe what's happening in space.
Newton-Cartan theory(one of two competing frameworks for understanding motion and gravity): A modern mathematical version of Newton's laws of motion that describes how objects move and gravity works in a way that connects to Einstein's later theories.

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