25 ideas
10041 | Impredicative Definitions refer to the totality to which the object itself belongs [Gödel] |
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] |
21716 | In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B] |
10751 | Second-order logic needs the sets, and its consequence has epistemological problems [Rossberg] |
10757 | Henkin semantics has a second domain of predicates and relations (in upper case) [Rossberg] |
10759 | There are at least seven possible systems of semantics for second-order logic [Rossberg] |
10035 | Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel] |
10753 | Logical consequence is intuitively semantic, and captured by model theory [Rossberg] |
10752 | Γ |- S says S can be deduced from Γ; Γ |= S says a good model for Γ makes S true [Rossberg] |
10754 | In proof-theory, logical form is shown by the logical constants [Rossberg] |
10042 | Reference to a totality need not refer to a conjunction of all its elements [Gödel] |
10756 | A model is a domain, and an interpretation assigning objects, predicates, relations etc. [Rossberg] |
10758 | If models of a mathematical theory are all isomorphic, it is 'categorical', with essentially one model [Rossberg] |
10761 | Completeness can always be achieved by cunning model-design [Rossberg] |
17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
10755 | A deductive system is only incomplete with respect to a formal semantics [Rossberg] |
10038 | A logical system needs a syntactical survey of all possible expressions [Gödel] |
10046 | The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel] |
17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
10039 | Some arithmetical problems require assumptions which transcend arithmetic [Gödel] |
17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
10043 | Mathematical objects are as essential as physical objects are for perception [Gödel] |
10045 | Impredicative definitions are admitted into ordinary mathematics [Gödel] |