Sentence examples for exactly one model from inspiring English sources

If a theory has, up to isomorphism, exactly one model, then it is said to be categorical.

In the second half of the nineteenth century Dedekind proved that the basic axioms of arithmetic have, up to isomorphism, exactly one model, and that the same holds for the basic axioms of Real Analysis.

In fact if T is a first-order theory with infinite models, then the strongest kind of categoricity we can hope for in T is that for certain infinite cardinals κ, T has exactly one model of cardinality κ, up to isomorphism.

The first important decision when designing a model is choosing what exactly one wants to model.

However, real data will likely not follow exactly one of the two models, but one of the models might give a better description of the data than the other.

In the Moran model, exactly one individual in the entire population is a newborn.

Unfortunately, in that model exactly one of each duplicate is immediately lost just after the duplication event, and the method proposed cannot be adapted because the underlying algorithms require that each marker synteny anchor be present only once in each genome.

The main idea here is to find the best decomposition of points of a protein into segments where each segment is described using exactly one of eight potential models.