Sentence examples for existence of a model from inspiring English sources

If ZFC is consistent, then it cannot prove the existence of a model of ZFC, for otherwise ZFC would prove its own consistency.

Again, a classical result of Specker establishes the existence of a model of NF in a suitable version of simple type theory with a formal counterpart of typical ambiguity.

Either T ′ proves ConT (the sentence of arithmetic expressing the consistency of T); or T ′ proves the existence of a model for (the axioms of) T. A vast range of mathematical theories can be, and have been, compared according to their consistency-strengths.

What's more, some of the results we'll examine later in this entry involve even stronger model-existence assumptions e.g., the existence of a transitive model for our axioms is strictly stronger than the mere existence of a model for our axioms.

There's been enough writing on the model-minority stereotype to fill an internet, but the gist is that the existence of a model minority is one of the mechanisms on which white supremacy depends and thrives.

Consequently, the existence of a model-free approach would be a great asset.

In formalisms that employ model-based reasoning mechanisms inconsistencies render a knowledge base useless due to the non-existence of a model.

Hereby, three fundamentally different cases are discussed: the availability of a complex, highly accurate model; the existence of a simplifying, the so-called short-cut model; and the non-existence of a model of any kind.

The country's gigantic oil wealth has taken the society from a simple, predominantly desert existence to a model of affluent consumerism in the space of a few decades.

(We just proved the existence of such a model in the previous paragraph, of course).

(Saucedo attempts to establish the existence of such a model more rigorously on the basis of some very weak possibility claims, but the argument is complex and resists compression).