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sav08:homework12 [2008/05/15 10:05] vkuncak |
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| ===== Optional Problem 3 ===== | ===== Optional Problem 3 ===== | ||
| - | Describe the set of all relations $r^s_F$ definable through singleton sets | + | Describe the set of all binary relations $r^s_F$ definable through singleton sets |
| \[ | \[ | ||
| r^s_F = \{(p,q) \mid F(\{p\},\{q\}) \} | r^s_F = \{(p,q) \mid F(\{p\},\{q\}) \} | ||
| \] | \] | ||
| - | where $F$ are formulas of W1S1. How does this set compare to the set of relations definable in Presburger arithmetic? | + | where $F$ are formulas of WS1S. How does this set compare to the set of all binary relations definable in Presburger arithmetic? |