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| Both sides previous revision Previous revision Next revision | Previous revision Next revision Both sides next revision | ||
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sav08:ground_terms [2008/04/01 15:55] giuliano |
sav08:ground_terms [2013/05/10 09:53] vkuncak |
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| **Example**\\ | **Example**\\ | ||
| - | ${\cal L}=\{a, f_1\}$ \\ | + | ${\cal L}=\{a, f\}$ \\ |
| $GT=\{a, f(a), f(f(a)), f(f(f(a))), ...\}$ | $GT=\{a, f(a), f(f(a)), f(f(f(a))), ...\}$ | ||
| Line 23: | Line 23: | ||
| Let $ar(f)=n$. Then $f : GT^n \to GT$ | Let $ar(f)=n$. Then $f : GT^n \to GT$ | ||
| - | $\alpha_H(f)(t_1,\ldots,t_n) =$ ++| $f(t_1,\ldots,t_n)$++ | + | $\alpha_H(f)(t_1,\ldots,t_n) = f(t_1,\ldots,t_n)$ |
| This defines $\alpha_H(f)$. How to define $\alpha_H(R)$ to ensure that elements of a set are true, i.e. that $e_S(S)(I_H) = {\it true}$?\\ | This defines $\alpha_H(f)$. How to define $\alpha_H(R)$ to ensure that elements of a set are true, i.e. that $e_S(S)(I_H) = {\it true}$?\\ | ||
| Partition $GT^n$ in two sets, one over which $\alpha_H(R)(t_1,...,t_n)$ is true and the other over which it is false. | Partition $GT^n$ in two sets, one over which $\alpha_H(R)(t_1,...,t_n)$ is true and the other over which it is false. | ||
| - | * is this possible for arbitrary set? ++| no ++ | + | * is this possible for arbitrary set? no |
| **Example** | **Example** | ||