Das System Q

Zusammenfassung

Die Axiome des Systems Q sind

$$ \begin{gathered} Q1{\text{ }}\forall x{\text{ }}x + \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{0} \dot = x \hfill \\ Q2{\text{ }}\forall x,{\text{ }}y x + S(y)\dot = S(x + y) \hfill \\ Q3{\text{ }}\forall x{\text{ }}x \cdot \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{0} \dot = \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{0} \hfill \\ Q4{\text{ }}\forall x,{\text{ }}y x \cdot S(y)\dot = x \cdot y + x \hfill \\ Q5{\text{ }}\forall x{\text{ }}\neg x < \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{0} \hfill \\ Q6{\text{ }}\forall x,{\text{ }}y x < S(y) \leftrightarrow (x\dot = y \vee x < y). \hfill \\ \end{gathered} $$