Sentence examples for countable model from inspiring English sources

Hence, it follows that (3) is true in some countable model.

Hence, if (3) has any model, it has a countable model, which is in fact a submodel of the original.

In particular, any L ω1,ω -sentence with an infinite model has a countable model.

How can a countable model satisfy the first-order sentence which "says that" there are uncountably many things?

More generally, for any two objects a and b, we can find a countable model M such that 1).

But it may still leave an obvious question unanswered: how can a countable model of ZFC satisfy such a formula?

Compared with standard RCC models given rise from regular connected spaces, these countable models have the nice property that each region can be constructed in finite steps from basic regions.

Secondly, he became aware that using essentially a first-order notion condemns the axiomatic system to countable models, the fundamental fact pointed out in Skolem (1923).

8. Skolem himself referred to the fact that set theory has countable models as the'relativity in set theory.' 9. See von Neumann 2005.

Hence, we conclude that under the condition (3.11) all p-adic quasi Gibbs measures corresponding to countable Potts model are described by those measures of q-state Potts model.

The first approach starts with a countable transitive model M of a sufficiently large fragment of ZFC and then (working in V) one actually builds an outer model M[G] that satisfies a large fragment of set theory and the statement one wishes to show is independent.