Full Idea
Putting multiplication together with addition and successor in the language of arithmetic produces incompleteness.
Gist of Idea
Incompleteness results in arithmetic from combining addition and successor with multiplication
Source
Peter Smith (Intro to Gödel's Theorems [2007], 10.7)
Book Reference
Smith,Peter: 'An Introduction to Gödel's Theorems' [CUP 2007], p.79
A Reaction
His 'Baby Arithmetic' has all three and is complete, but lacks quantification (p.51)