11 ideas
10882 | Predicative definitions only refer to entities outside the defined collection [Horsten] |
17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
10884 | A theory is 'categorical' if it has just one model up to isomorphism [Horsten] |
17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
10885 | Computer proofs don't provide explanations [Horsten] |
17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
10881 | The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten] |
15035 | If universals are not separate, we can isolate them by abstraction [Boethius, by Panaccio] |