more from Peter Smith

### Single Idea 10604

#### [catalogued under 6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic]

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)