undecidability of Russell's Principia Mathematica, there is a
fairly simple undecidable proposition namely, the proposition
*Undecidable*≡Halt<ExpressionFromString<Natural>>[RunOne.[]]
SelectOne.[i:Natural]≡ExpressionFromString<Natural>.[i] *finishesFirst* SelectOne.[i+1]
(expression1 *finishesFirst* expression2)
and expression2 evaluation finishes first.
The procedure SelectOne selects one of the expressions
created from strings.
For details see: https://papers.ssrn.com/abstract=3603021
Undecidable ≡ Halt<ExpressionFromString<Natural>>[⦅RunOne.[]⦆] is
inferentially undecidable in the theory Actors, that is,
⊬Undecidable and ⊬¬Undecidable where
RunOne.[]≡Eval.[SelectOne.[0]] and ⦅RunOne.[]⦆ is the
expression for the procedure application RunOne.[]
undecidability of Russell's Principia Mathematica, there is a
fairly simple undecidable proposition namely, the proposition
where RunOne.[]≡Eval.[SelectOne.[0]] such that Eval.[anExpression] evaluates anExpression and where the expression returns the value of whichever of the expressions expression1and expression2 evaluation finishes first.
The procedure SelectOne selects one of the expressions
created from strings.
For details see: https://papers.ssrn.com/abstract=3603021