The phrase "asserts the existence" is correct and usable in written English.
You can use it when discussing claims or statements that affirm or declare the presence of something.
Example: "The research paper asserts the existence of a previously unknown species in the rainforest."
Alternatives: "claims the presence" or "affirms the existence".
On the other hand, some constructions may share some syntactic features with the existential, but they should not be regarded as such: Lei (1993) lists three conditions for a clause to be called an existential: 1) Semantically, it asserts the existence of something, that is, there exists something (New) in someplace (Given).
For example, it asserts the existence of a set B corresponding to "Either x is an astronaut or x is a natural number".
Counsel contend that, by making a claim for profits, the claimant asserts the existence of the contract as opposed to its rescission; and that in such case the rule of damages, as settled is Speed's Case, 8 Wall.
The show borrows its title from E. A. Abbott's 1884 satire, in which a square asserts the existence of a third dimension and ends up in prison; it would have been nice to see a hint of such rebelliousness here.
Given any formula S x) that contains the letter x (and possibly others), Cantor's principle of abstraction asserts the existence of a set A such that, for each object x, x ∊ A if and only if S x) holds.
The axiom of choice has the feature not shared by other axioms of set theory that it asserts the existence of a set without ever specifying its elements or any definite way to select them.
If the Axiom of Infinity is reformulated to assert the existence of Vω , then the ranks proved to exist as sets by Zermelo set theory are exactly those which appear in the natural model Vω+ω of this theory.
The other was the 'inflationary' approach, which posited entities corresponding to all statements, thus 'creating' or asserting the existence of things that (Berlin believed) didn't exist at all.
This shows that for a solid sphere there exists (in the sense that the axioms assert the existence of sets) a decomposition into a finite number of pieces that can be reassembled to produce a sphere with twice the radius of the original sphere.
(A numerical sentence is a first-order sentence asserting the existence of some objects. For example, the numerical sentence that there exist at least two objects is: ∃x∃y(x ≠ y).) If van Inwagen is correct, it is indeterminate whether or not the relevant numerical sentence is true, in which case one of the constituent expressions—'∃', 'x', 'y', '~', '=' must be vague.
Several studies have asserted the existence of a strong and complex genetic component.
