display all the ideas for this combination of texts
3 ideas
15657 | To prove the consistency of set theory, we must go beyond set theory [Halbach] |
Full Idea: The consistency of set theory cannot be established without assumptions transcending set theory. | |
From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 2.1) |
13655 | The Löwenheim-Skolem theorems show that whether all sets are constructible is indeterminate [Putnam, by Shapiro] |
Full Idea: Putnam claims that the Löwenheim-Skolem theorems indicate that there is no 'fact of the matter' whether all sets are constructible. | |
From: report of Hilary Putnam (Models and Reality [1977]) by Stewart Shapiro - Foundations without Foundationalism | |
A reaction: [He refers to the 4th and 5th pages of Putnam's article] Shapiro offers (p.109) a critique of Putnam's proposal. |
9915 | V = L just says all sets are constructible [Putnam] |
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. | |
From: Hilary Putnam (Models and Reality [1977], p.425) |