User blog comment:Alemagno12/First Order Theory Theory/@comment-27513631-20170809194629/@comment-25601061-20170810175507

1. Fixed. Now T(n) can't be defined in theories.

2. FOTT doesn't prevent inconsistent theories and stuff like that, but FOTT(x) will never have an ill-defined value (unless there are no statements in FOTT x characters long that force at least one variable to have a well-defined value in order for that statement to be true)

3. Yes, it's supposed to be backwards, and I fixed it. Saying statements in T(n) are also statements in T(m) if n < m is the same as saying statements in T(n) are also statements in T(m) if T(n) < T(m), where T(n) > T(m) if n > m

4. It doesn't have to include X. It could be any symbol: Y, e, @, a banana emoji, etc. When we find a φ([statement/operator][symbol not defined for FOTT or in a theory < T][statement/operator]|[a theory T]) in a statement, the symbol is assumed to be a new operator defined in T.

5. Yes, T(n) contains all theories T(m) for m < n.