O.V. Belegradek, A.P. Stolboushkin and M.A. Taitslin. On order-generic queries. DIMACS Technical Report 95-56, December 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Corollary 3. NFO LG (Q; NFO LG (Q; 2 The proof technique given here is not restricted to continuous domains, or to o minimal structures. In fact, we can notice that the result applies to any domain such that Claim 5 holds for any internally presented structure. This was used in [5] to give the following result about the integers. Corollary 4. see [5] NFO LG (N; NFO LG (N; 2 This result is in contrast to [17] which proved that any computable query is definable in NFO(N; 0; 1) 6. EXPRESSIVENESS OF NONBOOLEAN QUERIES So far we have only considered ....

....given here is not restricted to continuous domains, or to o minimal structures. In fact, we can notice that the result applies to any domain such that Claim 5 holds for any internally presented structure. This was used in [5] to give the following result about the integers. Corollary 4. see [5]) NFO LG (N; NFO LG (N; 2 This result is in contrast to [17] which proved that any computable query is definable in NFO(N; 0; 1) 6. EXPRESSIVENESS OF NONBOOLEAN QUERIES So far we have only considered boolean queries given by first order sentences. This was enough to prove ....

O.V. Belegradek, A.P. Stolboushkin and M.A. Taitslin. On order-generic queries. DIMACS Technical Report 95-56, December 1995.

....Corollary 3 NFO LG (Q; NFO LG (Q; 2 The proof technique given here is not restricted to continuous domains, or to o minimal structures. In fact, we can notice that the result applies to any domain such that Claim 5 holds for any internally presented structure. This was used in [5] to give the following result about the integers. Corollary 4 (see [5] NFO LG (N; NFO LG (N; 2 This result is in contrast to [14] which proved that any computable query is definable in NFO(N; 0; 1) 6 Expressiveness of Nonboolean Queries So far we have only considered ....

....given here is not restricted to continuous domains, or to o minimal structures. In fact, we can notice that the result applies to any domain such that Claim 5 holds for any internally presented structure. This was used in [5] to give the following result about the integers. Corollary 4 (see [5]) NFO LG (N; NFO LG (N; 2 This result is in contrast to [14] which proved that any computable query is definable in NFO(N; 0; 1) 6 Expressiveness of Nonboolean Queries So far we have only considered boolean queries given by first order sentences. This was enough to prove ....

O.V. Belegradek, A.P. Stolboushkin and M.A. Taitslin. On order-generic queries. DIMACS Technical Report 95-56, December 1995.

....obtain the following result of [33] as a corollary. Corollary 3 NFO LG (Q; NFO LG (Q; 2 In contrast to [16] who proved that any computable query is definable in NFO(N; 0; 1) we can show the following using the techniques developed in the proof of theorem 4. Corollary 4 (cf. [5]) NFO LG (N; NFO LG (N; Proof. As noted in [5] we have the collapse of LG queries to queries using only the order relation in any model such that every type of an element over a hyperfinite set is countably generated. This can be shown by using the proof of theorem 4, since ....

....NFO LG (Q; NFO LG (Q; 2 In contrast to [16] who proved that any computable query is definable in NFO(N; 0; 1) we can show the following using the techniques developed in the proof of theorem 4. Corollary 4 (cf. 5] NFO LG (N; NFO LG (N; Proof. As noted in [5], we have the collapse of LG queries to queries using only the order relation in any model such that every type of an element over a hyperfinite set is countably generated. This can be shown by using the proof of theorem 4, since o minimality is only used in the proofs of claims 5 and 6. As shown ....

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O.V. Belegradek, A.P. Stolboushkin and M.A. Taitslin. On order-generic queries. DIMACS Technical Report 95-56, December 1995.

....the results in [6] is a generalization of our Corollary 5.8: graph connectivity and even cardinality are not expressible by any (not necessarily linear) real query sentence, both under the natural interpretation as under the active domain interpretation. ffl Belegradek, Stolboushkin and Taitslin [20, 21] have generalized Theorem 5.1 in another sense: instead of finite databases they considered possibly infinite databases definable by real formulas involving only simple inequalities. ffl Benedikt and Libkin [7] have shown that Theorem 4.11 holds in any densely ordered structure that satisfies the ....

O.V. Belegradek, A.P. Stolboushkin, and M.A. Taitslin. On ordergeneric queries. DIMACS Technical Report 96-01, 1996.

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O.V. Belegradek, A.P. Stolboushkin and M.A. Taitslin. On order-generic queries. DIMACS Technical Report 95-56, December 1995.

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