Name
Abstract | ||
|---|---|---|
We use Herbrand's theorem to give a new proof that Euclid's parallel axiom is not derivable from the other axioms of first-order Euclidean geometry. Previous proofs involve constructing models of non-Euclidean geometry. This proof uses a very old and basic theorem of logic together with some simple properties of ruler-and-compass constructions to give a short, simple, and intuitively appealing proof. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1017/bsl.2015.6 | BULLETIN OF SYMBOLIC LOGIC |
Keywords | Field | DocType |
geometry,Tarski,Euclid,Herbrand's theorem,parallel postulate | Discrete mathematics,Non-Euclidean geometry,Algebra,Point–line–plane postulate,Automated theorem proving,Absolute geometry,Pure mathematics,Herbrand's theorem,Mathematical proof,Euclidean geometry,Foundations of geometry,Mathematics | Journal |
Volume | Issue | ISSN |
21 | 2 | 1079-8986 |
Citations | PageRank | References |
1 | 0.37 | 1 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Michael Beeson | 1 | 22 | 4.09 |
| pierre boutry | 2 | 1 | 0.37 |
| Julien Narboux | 3 | 130 | 12.49 |