User:Vel!/Random

Define a language consisting of variable names 1, 2, 3, ... indexed by natural numbers, the number 0, and the operations S≤∃. All the operators are prefix (because I hate parentheses).

Important note: 0 is a literal and 1, 2, 3, ... are variables.


 * Sa is a + 1.
 * ≤ab is 1 if a ≤ b and 0 otherwise.
 * ∃ve is 1 if we can choose variable v such that expression e is true, 0 otherwise.

≤</tt> doubles as an, and the implication operator + zero form a functionally complete system. So it's possible to implement any Boolean operation using just these operators.


 * Negation: ≤a0</tt>
 * Negation: ≤a0</tt>