more from Peter Smith

Single Idea 10848

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

Full Idea

Multiplication in itself isn't is intractable. In 1929 Skolem showed a complete theory for a first-order language with multiplication but lacking addition (or successor). Multiplication together with addition and successor produces incompleteness.

Gist of Idea

Multiplication only generates incompleteness if combined with addition and successor


Peter Smith (Intro to Gödel's Theorems [2007], 10.7 n8)

Book Reference

Smith,Peter: 'An Introduction to Gödel's Theorems' [CUP 2007], p.79