structure for 'Formal Logic'    |     alphabetical list of themes    |     expand these ideas

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

[possible axiom saying all sets are constructible]

6 ideas
Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam]
Quine wants V = L for a cleaner theory, despite the scepticism of most theorists [Quine, by Shapiro]
The Löwenheim-Skolem theorems show that whether all sets are constructible is indeterminate [Putnam, by Shapiro]
V = L just says all sets are constructible [Putnam]
Constructibility: V = L (all sets are constructible) [Kunen]
If we accept that V=L, it seems to settle all the open questions of set theory [Hart,WD]