Mehrsortig ...Beispiel

Sorten: P, G, B, wobei [B] = Boolean

Signatur: I : P×G$ \to$B

Axiome:

    $\displaystyle \forall$x $\displaystyle \in$ P, y $\displaystyle \in$ P : x $\displaystyle \neq$ y$\displaystyle \implies$$\displaystyle \exists_{{=1}}^{}$z $\displaystyle \in$ G : I(x, z) $\displaystyle \wedge$ I(y, z)  
  $\displaystyle \wedge$ $\displaystyle \forall$x $\displaystyle \in$ G, y $\displaystyle \in$ G : x $\displaystyle \neq$ y$\displaystyle \implies$$\displaystyle \exists_{{=1}}^{}$z $\displaystyle \in$ P : I(z, x) $\displaystyle \wedge$ I(z, y)  
< < < < < < < sort.tex $\displaystyle \wedge$ $\displaystyle \exists$n $\displaystyle \in$ $\displaystyle \mathbb {N}$ : ($\displaystyle \forall$x $\displaystyle \in$ G : $\displaystyle \exists_{{=n}}^{}$y $\displaystyle \in$ P : I(y, x) $\displaystyle \wedge$ $\displaystyle \forall$x $\displaystyle \in$ G : $\displaystyle \exists_{{=n}}^{}$y $\displaystyle \in$ P : I(y, x))  
  $\displaystyle \wedge$ | P| = | G| = = = = = = =  
  $\displaystyle \wedge$ | P| = | G| $\displaystyle \wedge$ | P| $\displaystyle \neq$ $\displaystyle \emptyset$ > > > > > > > 1.2  

Finde je ein Modell mit n = 2, 3,...

Johannes Waldmann 2008-01-23