Sentence examples for countable from high-quality English sources.

• For the Thing Theorist “to be is to be countable.”

• Second, if it has countable models, it has models of any higher cardinality.

• Nick Mitchell's Northern Fail app took Northern Rail’s countless failures and made them countable (WIRED).

• Nothing is countable unless there exists a counter.

• Truth definition in L(ω1,ω) for a countable base language L.

• When L is countable, the situation is a little more involved.

• For infinite languages, they assumed an axiom of countable additivity for probabilities.

• On the assumption that T has a model, the Löwenheim-Skolem theorems ensure that it has a countable model.

Use countable in a sentence.

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

• S = ⟨U, F⟩ is a probabilistic space, with U countable and where F is a Boolean sub-algebra of the power set of U.

• Let A be a countable transitive set such that LA is a sublanguage of L(ω1, ω) and let Δ be a set of sentences of LA.

• It implies the axiom of choice for countable sets of sets but is incompatible with the unrestricted axiom of choice.

• Veblen in 1908 extended the initial segment of the countable for which fundamental sequences can be given effectively.

• The Löwenheim-Skolem theorem says that if a first-order theory has infinite models, then it has models whose domains are only countable.

• Its syntax is based upon two sets of symbols: a countable set Φ0 of atomic formulas and a countable set Π0 of atomic programs.

• The effect of abandoning even countable choice is the exclusion of many theorems that, as they stand, are proved using sequential, choice-based arguments.

countable sentence examples

• Kolmogorov comments that infinite probability spaces are idealized models of real random processes, and that he limits himself arbitrarily to only those models that satisfy countable additivity.

• The point Norton makes about the impossibility of a uniform distribution over a countable set of time intervals holds also for the time at which we might expect the space invader to occur in the second type of case.

• 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.

• As for set theory, the failure of categoricity was already taken note of by Skolem in 1923, because it follows from the Löwenheim-Skolem Theorem (which Skolem arrived at that year; see Skolem 1923, based on Löwenheim 1915 and Skolem 1920): any first order theory in a countable language that has a model has a countable model.