Full Idea
The neo-logicists take up Frege's claim that Hume's Principle introduces a new concept (of a number), but unlike Frege they go on to claim that it by itself gives a complete account of that concept.
Gist of Idea
Neo-logicists agree that HP introduces number, but also claim that it suffices for the job
Source
David Bostock (Philosophy of Mathematics [2009], 9.A.2)
Book Reference
Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.268
A Reaction
So the big difference between Frege and neo-logicists is the Julius Caesar problem.
Related Idea
Idea 18142 One-one correlations imply normal arithmetic, but don't explain our concept of a number [Frege, by Bostock]