User blog:Ubersketch/Weird axiomatic system

This axiomatic system assumes all of the axioms of ZFC. We then create a turing machine-based axiom schema designed like so: First, it counts up in base-6, using the Godel numbering outlined below, and checks the statement to see if it is an actual first-order (or other order?) statement. If it is, then it tries to prove that it is, or isn't implied by the current axioms. If it isn't, then it tries to see if it is consistent with the current axioms. If both conditions are met, then it is added to the axioms.

0: implication "→"

1: false "¬"

2: universal quantifier "∀"

3: variable separator "," e.g. "x,y"

4: membership "∈"

5: variables (5,55,555...) "x, y, z..."

Not sure why I made this, but it's a thing. Still waiting for Pbot's holy judgement. ​