<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>1409-2433</journal-id>
<journal-title><![CDATA[Revista de Matemática Teoría y Aplicaciones]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. Mat]]></abbrev-journal-title>
<issn>1409-2433</issn>
<publisher>
<publisher-name><![CDATA[Centro de Investigaciones en Matemática Pura y Aplicada (CIMPA) y Escuela de Matemática, San José, Costa Rica.]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1409-24332019000200179</article-id>
<article-id pub-id-type="doi">10.15517/rmta.v26i2.33639</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Definable groups in DCFA]]></article-title>
<article-title xml:lang="es"><![CDATA[Grupos definibles en DCFA]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Bustamante-Medina]]></surname>
<given-names><![CDATA[Ronald F.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad de Costa Rica Centro de Investigación en Matemática Pura y Aplicada (CIMPA) y Escuela de Matemática ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Costa Rica</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2019</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2019</year>
</pub-date>
<volume>26</volume>
<numero>2</numero>
<fpage>179</fpage>
<lpage>195</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S1409-24332019000200179&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S1409-24332019000200179&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S1409-24332019000200179&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract E. Hrushovski proved that the theory of difference-differential fields of characteristic zero has a model-companion. We denote it DCFA. In this paper we study definable abelian groups in a model of DCFA. First we prove that such a group is embeddable on an algebraic group. Then, we study one-basedeness, stability and stable embeddability of abelian definable groups.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen E. Hrushovski demostró que la teoría de cuerpos diferenciables de diferencia de característica cero tiene una modelo-compañera. La denotamos DCFA. En este artículo estudiamos los grupos abelianos en un modelo de DCFA. Primero demostramos que tales grupos son isomorfos a un subgrupo de un grupo algebraico. Posteriormente, estudiaremos las propiedades de ser monobasados, estables y establemente inmersibles de grupos definibles abelianos.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[model theory of fields]]></kwd>
<kwd lng="en"><![CDATA[supersimple theories]]></kwd>
<kwd lng="en"><![CDATA[difference-differential fields]]></kwd>
<kwd lng="en"><![CDATA[definable goups]]></kwd>
<kwd lng="en"><![CDATA[abelian groups]]></kwd>
<kwd lng="es"><![CDATA[teoría de modelos de cuerpos]]></kwd>
<kwd lng="es"><![CDATA[teorías supersimples]]></kwd>
<kwd lng="es"><![CDATA[cuerpos diferenciales de diferencia]]></kwd>
<kwd lng="es"><![CDATA[grupos definibles]]></kwd>
<kwd lng="es"><![CDATA[grupos abelianos.]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[R]]></surname>
<given-names><![CDATA[Bustamante]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Differentially closed fields of characteristic zero with a generic automorphism]]></article-title>
<source><![CDATA[Revista de Matemática: Teor&#305;&#769;a y Aplicaciones]]></source>
<year>2007</year>
<volume>14</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>81-100</page-range></nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[R]]></surname>
<given-names><![CDATA[Bustamante]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Algebraic jet spaces and Zilber&#8217;s dichotomy in DCFA]]></article-title>
<source><![CDATA[Revista de Matemática: Teor&#305;&#769;a y Aplicaciones]]></source>
<year>2010</year>
<volume>17</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>1-12</page-range></nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[R]]></surname>
<given-names><![CDATA[Bustamante]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Rank and dimension in difference-differential fields]]></article-title>
<source><![CDATA[Notre Dame Journal of Formal Logic]]></source>
<year>2011</year>
<volume>52</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>403-14</page-range></nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[R]]></surname>
<given-names><![CDATA[Bustamante]]></given-names>
</name>
</person-group>
<source><![CDATA[Arc spaces and Zilber&#8217;s dichotomy in dcfa]]></source>
<year>2019</year>
</nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Z]]></surname>
<given-names><![CDATA[Chatzidakis]]></given-names>
</name>
<name>
<surname><![CDATA[E]]></surname>
<given-names><![CDATA[Hrushovski]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Model theory of difference fields]]></article-title>
<source><![CDATA[Trans. Amer. Math. Soc]]></source>
<year>1999</year>
<volume>351</volume>
<numero>8</numero>
<issue>8</issue>
<page-range>2997-3071</page-range></nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Z]]></surname>
<given-names><![CDATA[Chatzidakis]]></given-names>
</name>
<name>
<surname><![CDATA[A]]></surname>
<given-names><![CDATA[Pillay]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Generic structures and simple theories]]></article-title>
<source><![CDATA[Ann. Pure Appl. Logic]]></source>
<year>1998</year>
<volume>95</volume>
<numero>1-3</numero>
<issue>1-3</issue>
<page-range>71-92</page-range></nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[E]]></surname>
<given-names><![CDATA[Hrushovski]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Unidimensional theories are superstable]]></article-title>
<source><![CDATA[Ann. Pure Appl. Logic]]></source>
<year>1990</year>
<volume>50</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>117-37</page-range></nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[E]]></surname>
<given-names><![CDATA[Hrushovski]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The Manin-Mumford conjecture and the model theory of difference fields]]></article-title>
<source><![CDATA[Ann. Pure Appl. Logic]]></source>
<year>2001</year>
<volume>112</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>43-115</page-range></nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[P]]></surname>
<given-names><![CDATA[Kowalski]]></given-names>
</name>
<name>
<surname><![CDATA[A]]></surname>
<given-names><![CDATA[Pillay]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A note on groups definable in difference fields]]></article-title>
<source><![CDATA[Proc. Amer. Math. Soc]]></source>
<year>2001</year>
<volume>130</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>205-12</page-range></nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[S]]></surname>
<given-names><![CDATA[Lang]]></given-names>
</name>
</person-group>
<source><![CDATA[Abelian Varieties, reprint of the 1959 original]]></source>
<year>1983</year>
<publisher-loc><![CDATA[New York ]]></publisher-loc>
<publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[D]]></surname>
<given-names><![CDATA[Marker]]></given-names>
</name>
</person-group>
<source><![CDATA[Connections between model theory and algebraic and analytic geometry]]></source>
<year>2000</year>
<volume>6</volume>
<publisher-loc><![CDATA[Caserta ]]></publisher-loc>
<publisher-name><![CDATA[Dipartimento di Matematica della Seconda Univ. di Napoli]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[A]]></surname>
<given-names><![CDATA[Pillay]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Some foundational questions concerning differential algebraic groups]]></article-title>
<source><![CDATA[Pacific J. Math]]></source>
<year>1997</year>
<volume>179</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>179-200</page-range></nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[A]]></surname>
<given-names><![CDATA[Pillay]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Definability and definable groups in simple theories]]></article-title>
<source><![CDATA[J. Symbolic Logic]]></source>
<year>1998</year>
<volume>63</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>788-96</page-range></nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[F,O]]></surname>
<given-names><![CDATA[Wagner]]></given-names>
</name>
</person-group>
<source><![CDATA[Simple Theories]]></source>
<year>2000</year>
<publisher-loc><![CDATA[Dordrecht ]]></publisher-loc>
<publisher-name><![CDATA[Kluwer Academic Publishers]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B15">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[F,O]]></surname>
<given-names><![CDATA[Wagner]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Some remarks on one-basedness]]></article-title>
<source><![CDATA[J. Symbolic Logic]]></source>
<year>2004</year>
<volume>69</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>34-8</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
