Hartry Field's nominalist program demonstrates that mathematical structures like G-structures can be dispensable posits rather than ontologically robust entities that 'persist' through physical change.

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Dispensable posits(describing what mathematical structures might be according to Field): Assumptions or things we initially include in our theories that turn out to be unnecessary—we can explain everything without them.
G-structures(Used to characterize affine and projective spacetime structures and explain their indestructibility): Spacetime structures, such as the affine and projective structures, that may be flat or non-flat but can never vanish.
Hartry Field(the author of the nominalist program discussed): A contemporary philosopher who developed a theory showing that we might not actually need to believe in abstract objects (like numbers) even though they seem useful in science and math.
Ontologically robust(contrasting with the idea that math structures are just helpful ideas): Something that genuinely, really exists as a real entity in the world, rather than being just a useful fiction or tool we invented.

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