Single Idea 9942

[catalogued under 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L]

Full Idea

Gödel proved the classical relative consistency of the axiom V = L (which implies the axiom of choice and the generalized continuum hypothesis). This established the full independence of the continuum hypothesis from the other axioms.

Gist of Idea

Gödel proved the classical relative consistency of the axiom V = L

Source

report of Kurt Gödel (What is Cantor's Continuum Problem? [1964]) by Hilary Putnam - Mathematics without Foundations

Book Reference

'Philosophy of Mathematics: readings (2nd)', ed/tr. Benacerraf/Putnam [CUP 1983], p.304


A Reaction

Gödel initially wanted to make V = L an axiom, but the changed his mind. Maddy has lots to say on the subject.