First-Order Queries over One Unary Function
... acyclic conjunctive queries [Yan81,PY99], or for full first-order queries on relational structures of bounded degree [See96,DG06,Lin06] or on tree-decomposable structures [FG01] (see also [FFG02]). A quasi-unary signature consists of one unary function and any number of monadic predicates. First-or ...
... acyclic conjunctive queries [Yan81,PY99], or for full first-order queries on relational structures of bounded degree [See96,DG06,Lin06] or on tree-decomposable structures [FG01] (see also [FFG02]). A quasi-unary signature consists of one unary function and any number of monadic predicates. First-or ...
Section 9.3: Mathematical Induction
... Comparing 36 = 729 and 100(6) = 600, we see 36 > 100(6) as required. Next, we assume that P (k) is true, that is we assume 3k > 100k. We need to show that P (k + 1) is true, that is, we need to show 3k+1 > 100(k + 1). Since 3k+1 = 3 · 3k , the induction hypothesis gives 3k+1 = 3 · 3k > 3(100k) = 300 ...
... Comparing 36 = 729 and 100(6) = 600, we see 36 > 100(6) as required. Next, we assume that P (k) is true, that is we assume 3k > 100k. We need to show that P (k + 1) is true, that is, we need to show 3k+1 > 100(k + 1). Since 3k+1 = 3 · 3k , the induction hypothesis gives 3k+1 = 3 · 3k > 3(100k) = 300 ...
![A Note on Locally Nilpotent Derivations and Variables of k[X,Y,Z]](http://s1.studyres.com/store/data/005260578_1-37b1c4bbe55693dae2b5b98fbc2c091d-300x300.png)
Strong Logics of First and Second Order
... To strengthen the logic one narrows the class of test structures hM, Si that are consulted, only now there are two dimensions—one can restrict the firstorder domain M and one can restrict the second-order domain S. The first restriction parallels the first-order case. But even if one allows all poss ...
... To strengthen the logic one narrows the class of test structures hM, Si that are consulted, only now there are two dimensions—one can restrict the firstorder domain M and one can restrict the second-order domain S. The first restriction parallels the first-order case. But even if one allows all poss ...
