Full Idea
'Set-theoretic' structuralism rejects deductive nominalism in favour of a background theory of sets, and mathematics as the various structures realized among the sets. This is often what mathematicians have in mind when they talk about structuralism.
Gist of Idea
'Set-theoretic' structuralism treats mathematics as various structures realised among the sets
Source
Øystein Linnebo (Structuralism and the Notion of Dependence [2008], I)
Book Reference
-: 'The Philosophical Quarterly' [-], p.61
A Reaction
This is the big shift from 'mathematics can largely be described in set theory' to 'mathematics just is set theory'. If it just is set theory, then which version of set theory? Which axioms? The safe iterative conception, or something bolder?
Related Ideas
Idea 14084 Non-eliminative structuralism treats mathematical objects as positions in real abstract structures [Linnebo]
Idea 14085 'Deductivist' structuralism is just theories, with no commitment to objects, or modality [Linnebo]
Idea 14086 'Modal' structuralism studies all possible concrete models for various mathematical theories [Linnebo]