Matches in SemOpenAlex for { <https://semopenalex.org/work/W1615580298> ?p ?o ?g. }
Showing items 1 to 77 of
77
with 100 items per page.
- W1615580298 abstract "In this note, we study non-standard models of the rational numbers with countably many elements. These are ordered fields, and so it makes sense to complete them, using non-standard Cauchy sequences. The main result of this note shows that these completions are real closed, i.e. each positive number is a square, and each polynomial of odd degree has a root. This way, we give a direct proof of a consequence of a theorem of Hauschild. In a previous version of this note, not being aware of these results, we missed to mention this reference. We thank Matthias Aschenbrenner for pointing out this and related work. We also give some information about the set of real parts of the finite elements of such completions -about the more interesting results along this we have been informed by Matthias Aschenbrenner. The main idea to achieve the results relies on a way to describe real zeros of a polynomial in terms of first order logic. This is achieved by carefully using the sign changes of such a polynomial." @default.
- W1615580298 created "2016-06-24" @default.
- W1615580298 creator A5001443442 @default.
- W1615580298 creator A5015448345 @default.
- W1615580298 creator A5080948362 @default.
- W1615580298 date "2006-04-21" @default.
- W1615580298 modified "2023-09-27" @default.
- W1615580298 title "Completions of countable non-standard models of Q" @default.
- W1615580298 hasPublicationYear "2006" @default.
- W1615580298 type Work @default.
- W1615580298 sameAs 1615580298 @default.
- W1615580298 citedByCount "0" @default.
- W1615580298 crossrefType "posted-content" @default.
- W1615580298 hasAuthorship W1615580298A5001443442 @default.
- W1615580298 hasAuthorship W1615580298A5015448345 @default.
- W1615580298 hasAuthorship W1615580298A5080948362 @default.
- W1615580298 hasConcept C10138342 @default.
- W1615580298 hasConcept C110729354 @default.
- W1615580298 hasConcept C118615104 @default.
- W1615580298 hasConcept C121332964 @default.
- W1615580298 hasConcept C134306372 @default.
- W1615580298 hasConcept C135692309 @default.
- W1615580298 hasConcept C139676723 @default.
- W1615580298 hasConcept C162324750 @default.
- W1615580298 hasConcept C177264268 @default.
- W1615580298 hasConcept C182306322 @default.
- W1615580298 hasConcept C199360897 @default.
- W1615580298 hasConcept C24890656 @default.
- W1615580298 hasConcept C2524010 @default.
- W1615580298 hasConcept C2775997480 @default.
- W1615580298 hasConcept C33923547 @default.
- W1615580298 hasConcept C41008148 @default.
- W1615580298 hasConcept C90119067 @default.
- W1615580298 hasConceptScore W1615580298C10138342 @default.
- W1615580298 hasConceptScore W1615580298C110729354 @default.
- W1615580298 hasConceptScore W1615580298C118615104 @default.
- W1615580298 hasConceptScore W1615580298C121332964 @default.
- W1615580298 hasConceptScore W1615580298C134306372 @default.
- W1615580298 hasConceptScore W1615580298C135692309 @default.
- W1615580298 hasConceptScore W1615580298C139676723 @default.
- W1615580298 hasConceptScore W1615580298C162324750 @default.
- W1615580298 hasConceptScore W1615580298C177264268 @default.
- W1615580298 hasConceptScore W1615580298C182306322 @default.
- W1615580298 hasConceptScore W1615580298C199360897 @default.
- W1615580298 hasConceptScore W1615580298C24890656 @default.
- W1615580298 hasConceptScore W1615580298C2524010 @default.
- W1615580298 hasConceptScore W1615580298C2775997480 @default.
- W1615580298 hasConceptScore W1615580298C33923547 @default.
- W1615580298 hasConceptScore W1615580298C41008148 @default.
- W1615580298 hasConceptScore W1615580298C90119067 @default.
- W1615580298 hasLocation W16155802981 @default.
- W1615580298 hasOpenAccess W1615580298 @default.
- W1615580298 hasPrimaryLocation W16155802981 @default.
- W1615580298 hasRelatedWork W1701701809 @default.
- W1615580298 hasRelatedWork W2005038809 @default.
- W1615580298 hasRelatedWork W2038078121 @default.
- W1615580298 hasRelatedWork W2130443256 @default.
- W1615580298 hasRelatedWork W2293517510 @default.
- W1615580298 hasRelatedWork W2323500172 @default.
- W1615580298 hasRelatedWork W2328435434 @default.
- W1615580298 hasRelatedWork W2497024078 @default.
- W1615580298 hasRelatedWork W2744309868 @default.
- W1615580298 hasRelatedWork W2950446711 @default.
- W1615580298 hasRelatedWork W2951189604 @default.
- W1615580298 hasRelatedWork W2952187757 @default.
- W1615580298 hasRelatedWork W3047551150 @default.
- W1615580298 hasRelatedWork W32971838 @default.
- W1615580298 hasRelatedWork W378808387 @default.
- W1615580298 hasRelatedWork W410898503 @default.
- W1615580298 hasRelatedWork W81094231 @default.
- W1615580298 hasRelatedWork W94356243 @default.
- W1615580298 hasRelatedWork W1516689377 @default.
- W1615580298 hasRelatedWork W2395467060 @default.
- W1615580298 isParatext "false" @default.
- W1615580298 isRetracted "false" @default.
- W1615580298 magId "1615580298" @default.
- W1615580298 workType "article" @default.