A Decision Method for Elementary Algebra and Geometry¶
Tarski, A. (1951). A Decision Method for Elementary Algebra and Geometry. University of California Press.
Cited by¶
1 citation across 1 artifact.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Decidability Computability
- The failure taxonomy completes the picture from the logic side: the provable formulas of first-order logic are semi-decidable — proof search halts with "yes" on every theorem but may loop forever on a non-theorem — and the theory of real-closed fields is decidable yet its decision procedure is doubly-exponential, so "decidable" never means "cheap."
This sourceProves the theory of real-closed fields (elementary geometry over the reals) decidable by quantifier elimination, with a high-complexity decision procedure.
- The failure taxonomy completes the picture from the logic side: the provable formulas of first-order logic are semi-decidable — proof search halts with "yes" on every theorem but may loop forever on a non-theorem — and the theory of real-closed fields is decidable yet its decision procedure is doubly-exponential, so "decidable" never means "cheap."
Verification¶
Does it exist? Not checked yet. This entry carries no identifier to resolve. It was extracted from the citation as written in the article, normalized, and deduplicated against the rest of the registry.
Does it back the claim? Not recorded. The single citation of this work carries no recorded support check.
Support is checked per citation rather than per work — the same source can be cited soundly in one article and wrongly in another. Per-citation recording began recently, so a citation with no recorded check is a gap in the record rather than evidence it went unchecked.
See how references were verified.
Registry ID ref:7b906a52f13b · see in the full table