Sentence examples for Under this relation from inspiring English sources

Under this relation the space of possible mathematical systems forms an intricate hierarchy of increasingly strong systems.

This is an equivalence relation on the hyperreal line: for each hyperreal a we write μ(a) for the equivalence class of a under this relation and call it the monad of a.

It is also easy to see that the classes \ \textbf{P}, \textbf{NP}, \textbf{PSPACE},\textbf{EXP}, \textbf{NEXP}\) and \ \textbf{EXPSPACE}\) are closed under this relation.[16] A problem \(Y\) is said to be hard for a class \ \textbf{C}\) if \(X \leq_P Y\) for all \(X \in \textbf{C}\).

If so, does blueness "fall under" this universal in the same sense as the sense in which a copy of Philosophical Studies falls under blueness?) Now what can we say about this relation, this "falling under"?

At the same time, upper approximation and lower approximation are defined under this improved relation.

1. Probably the best all-purpose understanding of what logics are would take them as equivalence classes of proof systems under the relation of having mutually interderivable rules, though even this ignores issues about translational equivalence across differing languages.

One very general way to investigate the space of possible mathematical systems is under the relation of interpretability.

The interpretability hierarchy is the collection of all theories (satisfying our three simplifying assumptions) ordered under the relation ≤.

A binary relation (mathcal{R}) is called complete if every elements are comparable under that relation (i.e., ([x,y]in mathcal{R}) (forall x,yin X)).

If she does so, then she indirectly ascribes the property of being hungry to Bill, under the relation of being a man uniquely seen.

In other words, [ j] is the equivalence class of vertex j under the relation of strong connectivity, as defined above.