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#existence_theorem

Existence theorem

Theorem which asserts the existence of an object

In mathematics, an existence theorem is a theorem which asserts the existence of a certain object. It might be a statement which begins with the phrase "there exist(s)", or it might be a universal statement whose last quantifier is existential. In the formal terms of symbolic logic, an existence theorem is a theorem with a prenex normal form involving the existential quantifier, even though in practice, such theorems are usually stated in standard mathematical language. For example, the statement that the sine function is continuous everywhere, or any theorem written in big O notation, can be considered as theorems which are existential by nature—since the quantification can be found in the definitions of the concepts used.

Tue 16th

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Existence theorem Picard–Lindelöf theorem Peano existence theorem Carathéodory's existence theorem Gödel's completeness theorem Kolmogorov extension theorem Von Neumann–Bernays–Gödel set theory Nash equilibrium Algebraic geometry and analytic geometry Grothendieck existence theorem

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