display all the ideas for this combination of texts
2 ideas
10132 | There can be no single consistent theory from which all mathematical truths can be derived [Gödel, by George/Velleman] |
Full Idea: Gödel's far-reaching work on the nature of logic and formal systems reveals that there can be no single consistent theory from which all mathematical truths can be derived. | |
From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.8 |
17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
Full Idea: Some of the standard large cardinals (in order of increasing (logical) strength) are: inaccessible, Mahlo, weakly compact, indescribable, Erdös, measurable, strong, Wodin, supercompact, huge etc. (...and ineffable). | |
From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) | |
A reaction: [I don't understand how cardinals can have 'logical strength', but I pass it on anyway] |