Sentence examples for countable level from inspiring English sources

Since every countable level is itself countable (after all, there are only countably many possible defining formulas), and there are ω1 countable levels, there must be only ω1 real numbers.

Thus A is constructible on a countable level, which was to have been shown.

The difficulty here, if not of the whole proof altogether, lies in showing that every real is constructed already on a countable level of the L-hierarchy.

As concerns the CH, the idea behind the proof of it in L is simply the following: Gödel showed that assuming V = L, every real number occurs on some countable level of the L-hierarchy.

However, we show that even though the usual set R of real numbers can be represented as the branch space of a tree with countable height and countable levels, most subsets of R cannot be represented in this way.

However, it should be understood that because spore survivability assays entail growing surviving spores to countable levels in liquid or solid media, resistance mechanisms at any stage of growth may be important to survivability.

In addition, SS was still at countable levels on egg shells after two-week storage, suggesting that SS may have an advantage in survival and particularly under refrigeration conditions.

Furthermore, while at all levels < ω1, the collection of predicates is countable, the collection of predicates at level ω1 is of cardinality ω1.

In 1905 Lebesgue studied the Borel sets in an epochal memoir, showing that their hierarchy has levels for all countable ordinals, and analyzing the Baire functions as counterparts of the Borel sets.

When this turned out not to be an issue, the infectious dose was raised to 10 CFU to increase lung infection levels, yield more countable colonies, and allow the effects of a range of infectious doses to be examined.

The weak form of the eigenvalue problem reads (10.17) a (u, v ) = λ b (u, v ) for all  v ∈ V. On the continuous level, there exists a countable number of such Eigenpairs with positive eigenvalues ordered increasingly which essentially depend on the polyhedral bounded Lipschitz domain Ω ⊂ R d.