SWhat changed
Tarski gave an effective procedure converting first-order real-algebra formulas built from polynomial equations, inequalities and logical quantifiers into equivalent quantifier-free formulas. For closed sentences this yields a terminating truth-decision method; coordinate translation gives a corresponding decision method for elementary Euclidean geometry.
Scientific scope
Tarski gave an effective procedure converting first-order real-algebra formulas built from polynomial equations, inequalities and logical quantifiers into equivalent quantifier-free formulas. For closed sentences this yields a terminating truth-decision method; coordinate translation gives a corresponding decision method for elementary Euclidean geometry. The language ranges over real numbers with ordered-ring operations and encodable constants, not arbitrary sets/functions, unrestricted integer quantifiers or every theorem of mathematics. Parameters can remain free in a quantifier-free output; this is not a decision oracle for arbitrary uncomputably specified real coefficients. Adding an integer predicate or sine is explicitly outside the decidable language. The report does not supply a practical uniform runtime guarantee, an implementation or a resolution of real exponentiation. Fixed-size instances do not prove a variable-size universal conjecture.
Evidence
The linked original works support the scoped statement and contribution attribution. WRS has not independently replayed experiments or reconstructed a full mathematical proof. The language ranges over real numbers with ordered-ring operations and encodable constants, not arbitrary sets/functions, unrestricted integer quantifiers or every theorem of mathematics. Parameters can remain free in a quantifier-free output; this is not a decision oracle for arbitrary uncomputably specified real coefficients. Adding an integer predicate or sine is explicitly outside the decidable language. The report does not supply a practical uniform runtime guarantee, an implementation or a resolution of real exponentiation. Fixed-size instances do not prove a variable-size universal conjecture.
Contributors
- The named authors in the research record · SCIENCE: Source-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. Individual effort shares and unresolved identities are not inferred.
Provisional WRS assessment, edition 2026-10-23.3. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
Full scientific record · Browse contribution grades · Request a correction