Full Idea
The 'deductivist' version of eliminativist structuralism avoids ontological commitments to mathematical objects, and to modal vocabulary. Mathematics is formulations of various (mostly categorical) theories to describe kinds of concrete structures.
Clarification
'Categorical' means they all map onto one another
Gist of Idea
'Deductivist' structuralism is just theories, with no commitment to objects, or modality
Source
Øystein Linnebo (Structuralism and the Notion of Dependence [2008], 1)
Book Reference
-: 'The Philosophical Quarterly' [-], p.60
A Reaction
'Concrete' is ambiguous here, as mathematicians use it for the actual working maths, as opposed to the metamathematics. Presumably the structures are postulated rather than described. He cites Russell 1903 and Putnam. It is nominalist.
Related Ideas
Idea 14084 Non-eliminative structuralism treats mathematical objects as positions in real abstract structures [Linnebo]
Idea 14086 'Modal' structuralism studies all possible concrete models for various mathematical theories [Linnebo]
Idea 14087 'Set-theoretic' structuralism treats mathematics as various structures realised among the sets [Linnebo]