more from this thinker     |     more from this text

Single Idea 9915

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

Full Idea

V = L just says all sets are constructible. L is the class of all constructible sets, and V is the universe of all sets.

Gist of Idea

V = L just says all sets are constructible

Source

Hilary Putnam (Models and Reality [1977], p.425)

Book Ref

'Philosophy of Mathematics: readings (2nd)', ed/tr. Benacerraf/Putnam [CUP 1983], p.425

The 6 ideas with the same theme [possible axiom saying all sets are constructible]:

9942 Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam]
10211 Quine wants V = L for a cleaner theory, despite the scepticism of most theorists [Quine, by Shapiro]
13655 The Löwenheim-Skolem theorems show that whether all sets are constructible is indeterminate [Putnam, by Shapiro]
9915 V = L just says all sets are constructible [Putnam]
13040 Constructibility: V = L (all sets are constructible) [Kunen]
13516 If we accept that V=L, it seems to settle all the open questions of set theory [Hart,WD]