Full Idea
The nonconservativeness of set theory over first-order arithmetic has done much to establish set theory as a substantial theory indeed.
Clarification
'Nonconservative' means it enables new proofs
Gist of Idea
Set theory is substantial over first-order arithmetic, because it enables new proofs
Source
Leon Horsten (The Tarskian Turn [2011], 07.5)
Book Reference
Horsten,Leon: 'The Tarskian Turn' [MIT 2011], p.93
A Reaction
Horsten goes on to point out the price paid, which is the whole new ontology which has to be added to the arithmetic. Who cares? It's all fictions anyway!