19391 | We can assign a characteristic number to every single object [Leibniz] |
17888 | The undecidable sentence can be decided at a 'higher' level in the system [Gödel] |
17883 | Gödel's Theorems did not refute the claim that all good mathematical questions have answers [Gödel, by Koellner] |
10770 | If completeness fails there is no algorithm to list the valid formulas [Tharp] |
10609 | Two routes to Incompleteness: semantics of sound/expressible, or syntax of consistency/proof [Smith,P] |
10621 | Gödel's First Theorem sabotages logicism, and the Second sabotages Hilbert's Programme [Smith,P] |
17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
15353 | The first incompleteness theorem means that consistency does not entail soundness [Horsten] |
10755 | A deductive system is only incomplete with respect to a formal semantics [Rossberg] |
13852 | Axioms are ω-incomplete if the instances are all derivable, but the universal quantification isn't [Engelbretsen/Sayward] |