Matches in SemOpenAlex for { <https://semopenalex.org/work/W1862570265> ?p ?o ?g. }
Showing items 1 to 72 of
72
with 100 items per page.
- W1862570265 abstract "The paper is a continuation of our earlier article where we developed a theory of active and non-active infinitesimals and intended to establish quantifier elimination in quasianalytic structures. That article, however, did not attain full generality, which refers to one of its results, namely the theorem on an active infinitesimal, playing an essential role in our non-standard analysis. The general case was covered in our subsequent preprint, which constitutes a basis for the approach presented here. We also provide a quasianalytic exposition of the results concerning rectilinearization of terms and of definable functions from our earlier research. It will be used to demonstrate a quasianalytic structure corresponding to a Denjoy-Carleman class which, unlike the classical analytic structure, does not admit quantifier elimination in the language of restricted quasianalytic functions augmented merely by the reciprocal function. More precisely, we construct a plane definable curve, which indicates both that the classical theorem by J. Denef and L. van den Dries as well as L{}ojasiewicz's theorem that every subanalytic curve is semianalytic are no longer true for quasianalytic structures. Besides rectilinearization of terms, our construction makes use of some theorems on power substitution for Denjoy-Carleman classes and on non-extendability of quasianalytic function germs. The last result relies on Grothendieck's factorization and open mapping theorems for (LF)-spaces. Note finally that this paper comprises our earlier preprints on the subject from May 2012." @default.
- W1862570265 created "2016-06-24" @default.
- W1862570265 creator A5023160028 @default.
- W1862570265 date "2014-05-12" @default.
- W1862570265 modified "2023-09-27" @default.
- W1862570265 title "Quantifier elimination in quasianalytic structures via non-standard analysis" @default.
- W1862570265 cites W1487235877 @default.
- W1862570265 cites W1503042153 @default.
- W1862570265 cites W1594563152 @default.
- W1862570265 cites W1666726666 @default.
- W1862570265 cites W1974849843 @default.
- W1862570265 cites W2019569217 @default.
- W1862570265 cites W2020130865 @default.
- W1862570265 cites W2079526260 @default.
- W1862570265 cites W2110626664 @default.
- W1862570265 cites W2119232867 @default.
- W1862570265 cites W2765091900 @default.
- W1862570265 cites W2964256153 @default.
- W1862570265 cites W639777283 @default.
- W1862570265 hasPublicationYear "2014" @default.
- W1862570265 type Work @default.
- W1862570265 sameAs 1862570265 @default.
- W1862570265 citedByCount "0" @default.
- W1862570265 crossrefType "posted-content" @default.
- W1862570265 hasAuthorship W1862570265A5023160028 @default.
- W1862570265 hasConcept C118615104 @default.
- W1862570265 hasConcept C134306372 @default.
- W1862570265 hasConcept C136119220 @default.
- W1862570265 hasConcept C199343813 @default.
- W1862570265 hasConcept C202444582 @default.
- W1862570265 hasConcept C2777686260 @default.
- W1862570265 hasConcept C32278780 @default.
- W1862570265 hasConcept C33923547 @default.
- W1862570265 hasConcept C71924100 @default.
- W1862570265 hasConcept C91229774 @default.
- W1862570265 hasConceptScore W1862570265C118615104 @default.
- W1862570265 hasConceptScore W1862570265C134306372 @default.
- W1862570265 hasConceptScore W1862570265C136119220 @default.
- W1862570265 hasConceptScore W1862570265C199343813 @default.
- W1862570265 hasConceptScore W1862570265C202444582 @default.
- W1862570265 hasConceptScore W1862570265C2777686260 @default.
- W1862570265 hasConceptScore W1862570265C32278780 @default.
- W1862570265 hasConceptScore W1862570265C33923547 @default.
- W1862570265 hasConceptScore W1862570265C71924100 @default.
- W1862570265 hasConceptScore W1862570265C91229774 @default.
- W1862570265 hasLocation W18625702651 @default.
- W1862570265 hasOpenAccess W1862570265 @default.
- W1862570265 hasPrimaryLocation W18625702651 @default.
- W1862570265 hasRelatedWork W1576358566 @default.
- W1862570265 hasRelatedWork W1820365790 @default.
- W1862570265 hasRelatedWork W1995742741 @default.
- W1862570265 hasRelatedWork W1997612982 @default.
- W1862570265 hasRelatedWork W2008428267 @default.
- W1862570265 hasRelatedWork W2071530339 @default.
- W1862570265 hasRelatedWork W2098464720 @default.
- W1862570265 hasRelatedWork W2142864310 @default.
- W1862570265 hasRelatedWork W2335028541 @default.
- W1862570265 hasRelatedWork W2598521301 @default.
- W1862570265 hasRelatedWork W2605394209 @default.
- W1862570265 hasRelatedWork W2760298040 @default.
- W1862570265 hasRelatedWork W2951670728 @default.
- W1862570265 hasRelatedWork W2956168385 @default.
- W1862570265 hasRelatedWork W2963700838 @default.
- W1862570265 hasRelatedWork W3103287392 @default.
- W1862570265 hasRelatedWork W336036677 @default.
- W1862570265 hasRelatedWork W636716712 @default.
- W1862570265 hasRelatedWork W79887696 @default.
- W1862570265 hasRelatedWork W2741514631 @default.
- W1862570265 isParatext "false" @default.
- W1862570265 isRetracted "false" @default.
- W1862570265 magId "1862570265" @default.
- W1862570265 workType "article" @default.