That is, a statement of the form:
- $\exists x: P \paren x$
In the existential statement:
- $\exists x: \map P x$
Thus, the meaning of $\exists x: \map P x$ does not change if $x$ is replaced by another symbol.
That is, $\exists x: \map P x$ means the same thing as $\exists y: \map P y$ or $\exists \alpha: \map P \alpha$. And so on.
A conditionally existential statement is an existential statement which states the existence of an object fulfilling a certain propositional function dependent upon the existence of certain other objects.
Also known as
An existential statement can also be referred to as a existential sentence, or more wordily, a sentence of an existential character.
- 1946: Alfred Tarski: Introduction to Logic and to the Methodology of Deductive Sciences (2nd ed.) ... (previous) ... (next): $\S 1.3$: Universal and Existential Sentences
- 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 3$: Statements and conditions; quantifiers