Full Idea
A model is created when a language is 'interpreted', by assigning non-logical terms to objects in a set, according to a 'true-in' relation, but we must bear in mind that this 'interpretation' does not associate anything like Fregean senses with terms.
Gist of Idea
When an 'interpretation' creates a model based on truth, this doesn't include Fregean 'sense'
Source
Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.131)
Book Reference
-: 'Journal of Philosophy' [-], p.131
A Reaction
This seems like a key point (also made by Hofweber) that formal accounts of numbers, as required by logic, will not give an adequate account of the semantics of number-terms in natural languages.