There exists a Theory of Identity in mathematical logic. I've encountered it for the first time in Principia Mathematica by Alfred North Whitehead and Bertrand Russell (1910). Quote: "This definition ...
Following Halmos's Naive Set Theory, Russell's Paradox emerges from using the axiom of specification (that for every set $A$ and property $\phi$ there exists a set $Y$ whose elements are those ...
As I understand it, undecidability means that there exists no proofs or contradictions of a statement. So if you've proved $X$ is undecidable then there are no contradictions to $X$, so $X$ always ...
The Russell paradox arise in the Cantor set theory, but it can be avoided in the $ZF$ and in $NGB$ axiomatic set theory. Are there other axiomatic set theories in which this paradox can be avoided? ...
Statements like A) A is false. or B1) B2 is true. B2) B1 is false. cannot be assigned a truth-value due to their ...