The much-studied theory PA, first-order Peano arithmetic, is of course obtained by using, in place of the second-order induction postulate ∀X[X0 & ∀y Xy → XSy) → ∀y Xy], the corresponding first-order schema φ(0) & ∀y(φ y → φ Sy)) → ∀y φ y) where φ can be any suitable first-order formula.
Although a specific example of the use of KEGs is presented as a means for structuring clinical information in an order set schema, KEGs can serve as building blocks for the definition of any schema, document, or template that can benefit from the extra dimensions KEGs add to data representation, indexing, and retrieval.
The approach for an order set schema based on KEGs is part of the infrastructure being installed at Partners for KM.
The performance of a N-body simulation with the second order leapfrog schema is 0.505 Gflops for N = 1984, which is more than 10 times faster than the performance of the host computer.
The orthographic similarities between the first-order induction schema and the second-order induction axiom have an unfortunate tendency to obscure the important differences between them.
That is, there are sentences of first-order arithmetic that can be deduced from the second-order induction axiom (together with the other axioms of arithmetic, which are common to first-order and second-order arithmetic) but not from the instances of the first-order induction schema (see Shapiro 1991: 110).
Nor are they inferentially equivalent: the set of instances of the first-order induction schema is logically weaker than the second-order induction axiom.
For example, in order to identify schema update methods, we first identify the declaration of variables.
Analysis, or second-order arithmetic, is the extension of first-order arithmetic with the comprehension schema for arbitrary second-order formulae.
Then, we analyzed our schema in order to identify which tables of the data warehouse provide such data.
