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Impossibility Theorem

Logic, Foundations and Set Theory

An impossibility theorem is a theorem that demonstrates a problem or general set of problems cannot be solved; such results are also known as proofs of impossibility, negative proofs or negative results. The cited article says they often resolve decades or centuries of work spent looking for a solution by proving there is no solution, that proving something is impossible is usually much harder than the opposite task because a proof must work in general rather than for one example, and that they are usually expressible as negative existential or universal propositions in logic. The irrationality of the square root of 2 is named as one of the oldest such proofs. Theorems that rule out a construction or solution are grouped under this concept.

Connections

In Branch

Logic and Foundations, Branches of Mathematics
Source Impossibility Theorem

Statement Form Of

Abel-Ruffini Theorem, Theorems
Angle Trisection, Theorems
Antidynamo Theorem, Theorems
Arrow's Impossibility Theorem, Theorems
Aumann's Agreement Theorem, Theorems
Bell's Theorem, Theorems
Borde-Guth-Vilenkin Theorem, Theorems
Bruck-Ryser-Chowla Theorem, Theorems
Church's Theorem, Theorems
Clausius Theorem, Theorems
Cohen's Independence Theorem, Theorems
Coleman-Mandula Theorem, Theorems
Duggan-Schwartz Theorem, Theorems
Elitzur's Theorem, Theorems
Entscheidungsproblem, Theorems
Erdos-Anning Theorem, Theorems
Gentzen's Consistency Proof, Theorems
Gibbard-Satterthwaite Theorem, Theorems
Godel's Incompleteness Theorems, Theorems
Greibach's Theorem, Theorems
Haag's Theorem, Theorems
Hairy Ball Theorem, Theorems
Holmstrom's Theorem, Theorems
Kochen-Specker Theorem, Theorems
Liberal Paradox, Theorems
McKelvey-Schofield Chaos Theorem, Theorems
Mermin-Wagner Theorem, Theorems
Myerson-Satterthwaite Theorem, Theorems
No Free Lunch Theorem, Theorems
No-Cloning Theorem, Theorems
Paris-Harrington Theorem, Theorems
Rice's Theorem, Theorems
Richardson's Theorem, Theorems
Scallop Theorem, Theorems
Solovay's Theorem, Theorems
Sonnenschein-Mantel-Debreu Theorem, Theorems
Tarski's Undefinability Theorem, Theorems
Tennenbaum's Theorem, Theorems
Time Hierarchy Theorem, Theorems
Trakhtenbrot's Theorem, Theorems
Turing's Proof, Theorems
Ugly Duckling Theorem, Theorems
Undecidability of the Halting Problem, Theorems
Vaught's Theorem, Theorems
Source Vaught Conjecture (Wikipedia)
Wedderburn's Little Theorem, Theorems
Wiles's Proof of Fermat's Last Theorem, Theorems
Sources
Impossibility Theorem
  • Wikipedia, lead section
    In mathematics, an impossibility theorem is a theorem that demonstrates a problem or general set of problems cannot be solved.
  • In Branch: Logic and Foundations, Lead section
    In mathematics, an impossibility theorem is a theorem that demonstrates a problem or general set of problems cannot be solved. These are also known as proofs of impossibility
View the Source
Vaught Conjecture (Wikipedia)
Statement Form Of: Vaught's Theorem, Section: Vaught's theorem
Quote, Statement Form Of: Vaught's Theorem, Section: Vaught's theorem
Vaught proved that the number of countable models of a complete theory cannot be 2.
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