W. Wechler. Universal Algebra for Computer Scientists. Number 25 in EATCS Monographs of Theoretical Computer Science. SpringerVerlag, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....d n 2 w implies d 2 w . If T is a set of such implications, we say that w w is a T model if w j= for all 2 T . There is an alternative characterization of T models that can be helpful in proving facts about termination relations (a closelyrelated characterization can be found in [35], page 22) Suppose w is a finite set and X P(w) Then X is a closure system if w 2 X, 2 X, and X is closed under intersection. Proposition 3 Suppose w is a finite set. Then X P(w) is a closure system iff there is a w termination theory T such that X is the set of T models. Proof: For ....

W. Wechler. Universal Algebra for Computer Scientists. Number 25 in EATCS Monographs in Theoretical Computer Science. Springer-Verlag,

....and the set above is finite because w is, w 0 must be in X . But since w # X and w # w 0 , it must be the case that there is a d w 0 such that d w # . Now consider the formula (w # d) Note that (w # T , and w # (w # d) Thus, w # Y , completing the proof. See [132], page 22 for the same proof. The proof is similar to a part of Sieber s proof that the sequentiality relations are precisely those that are closed under the operations of PCF [121] The second kind of relation is built from sets of sets of T models. If T is a w termination theory, define a ....

Wolgang Wechler. Universal Algebra for Computer Scientists. Number 25 in EATCS Monographs in Theoretical Computer Science. Springer-Verlag,

....w 0 implies d 2 w 0 . If T is a set of such implications, we say that w 0 w is a T model if w 0 j= y for all y 2 T . There is an alternative characterization of T models that can be helpful in proving facts about termination relations (a closely related characterization can be found in [35], page 22) Suppose w is a finite set and X P (w) Then X is a closure system if w 2 X , 0 2 X , and X is closed under intersection. Proposition 3 Suppose w is a finite set. Then X P (w) is a closure system iff there is a w termination theory T such that X is the set of T models. Proof: ....

W. Wechler. Universal Algebra for Computer Scientists. Number 25 in EATCS Monographs in Theoretical Computer Science. Springer-Verlag, 1992. 4 April

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W. Wechler. Universal Algebra for Computer Scientists. Number 25 in EATCS Monographs of Theoretical Computer Science. SpringerVerlag, 1992.

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