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Metamathematik von ZFC

  • Martin Ziegler
Part of the Mathematik Kompakt book series (MAKO, volume 0)

Zusammenfassung

Wir ordnen jeder L Me -Formel ψ eine Konstante ⌜ψ⌝ in einer definitorischen Erweiterung von ZFCzu (siehe Satz 8.1).Zunächst ordnen wir allen Zeichen einen Termzu:
$$ \begin{gathered} \left\lceil {\dot = } \right\rceil = (\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{0} ,\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{0} ) \hfill \\ \left\lceil \wedge \right\rceil = (\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{0} ,\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{0} ) \hfill \\ \left\lceil \neg \right\rceil = (\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{0} ,\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{2} ) \hfill \\ \left\lceil ( \right\rceil = (\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{0} ,\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{3} ) \hfill \\ \left\lceil ) \right\rceil = (\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{0} ,\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{4} ) \hfill \\ \left\lceil \exists \right\rceil = (\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{0} ,\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{5} ) \hfill \\ \left\lceil \varepsilon \right\rceil = (\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{0} ,\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{6} ) \hfill \\ \left\lceil {\nu _0 } \right\rceil = (\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{1} ,\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{0} ) \hfill \\ \left\lceil {\nu _1 } \right\rceil = (\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{1} ,\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{1} ) \hfill \\ \ldots = \ldots \hfill \\ \end{gathered} $$
Für eine Formel ψ=ζ0ζ1…ζn−1 der Länge n setzen wir
$$ \left\lceil \psi \right\rceil = \left\{ {(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{0} ,\left\lceil {\zeta _0 } \right\rceil ), \ldots ,(\underline {n - 1,} \left\lceil {\zeta _{n - 1} } \right\rceil )} \right\}. $$

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Copyright information

© Birkhäuser / Springer Basel AG 2010

Authors and Affiliations

  • Martin Ziegler
    • 1
  1. 1.Mathematisches InstitutUniversität FreiburgFreiburgDeutschland

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