18841 | Categoricity implies that Dedekind has characterised the numbers, because it has one domain [Rumfitt on Dedekind] |
10833 | Many concepts can only be expressed by second-order logic [Boolos] |
10294 | Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro] |
10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price] |
13701 | A single second-order sentence validates all of arithmetic - but this can't be proved axiomatically [Sider] |
10980 | Second-order arithmetic covers all properties, ensuring categoricity [Read] |
10979 | Although second-order arithmetic is incomplete, it can fully model normal arithmetic [Read] |
17899 | Second-order induction is stronger as it covers all concepts, not just first-order definable ones [George/Velleman] |
10674 | A plural language gives a single comprehensive induction axiom for arithmetic [Hossack] |