Sentence examples for closure operations from inspiring English sources

Closure operations as defined in the opening section are sometimes called closure operators.

Some authors discuss matters of logical theory placing a particular emphasis on closure operations and their systems of closed sets (sets X with C X) = X); see Pollard and Martin (1996) and references there cited.

Gödel started with three very simple functions, the initial functions, and two natural closure operations, composition and primitive recursion, each of which take some already defined functions and use them to define a new one.

In this case the derived closure operations Th ○ Mod (mapping S0 to Th(Mod(S0))) and Mod ○ Th (understood analogously) on S and T respectively deliver the set of first-order consequences of S0 and the set of all models verifying all the sentences verified by every M ∈ T0.

The direct/indirect precedence P total relation between operators can be inferred by applying the transitive closure operation to the P direct(n, n) matrix: P total = P direct ∪ P direct 2 ∪ ⋯ ∪ P direct i ∪ ⋯ ∪ P direct n, (2)  .

We introduce a new closure operation on natural numbers involving candelabra systems.

This new closure operation makes it possible to generalize various constructions for Steiner 3-designs and to create new infinite families of Steiner 2-designs and 3-designs.

The notation and denote the closure operation and convex hull operation on set, respectively.

We adopt the convention that the empty class ∅ is c-closed for every closure operation c.

These two facts imply that the reflexive transitive closure of >sc is reduction when the tonicity of the reflexive transitive closure operation (denoted by *) is taken into account.

The conditions given earlier for C's being a closure operation can be recast as conditions definitive of a consequence relation, conditions we do not give explicitly here.