Full Idea
Relativist Structuralism must first assume the existence of an infinite set, otherwise there would be no model to pick, and arithmetical terms would have no reference.
Gist of Idea
The existence of an infinite set is assumed by Relativist Structuralism
Source
E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4)
A Reaction
See Idea 10169 for Relativist Structuralism. They point out that ZFC has an Axiom of Infinity.
Related Idea
Idea 10169 Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price]