Classification of Formulas
The formulas of SA can be classified into four mutually exclusive categories:
- Formula F is a theorem if F can be derived, but not ~F.
- F is a falsehood if ~F can be derived, but not F.
- F is an introversion if ~F can be derived when F is assumed and F can be derived when ~F is assumed.
- F is a profundity if neither F nor ~F can be derived, and F is not an introversion.
It is known that any consistency statement about SA is an introversion and Continuum Hypothesis is a profundity.