<?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>S1409-24332014000100001</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Objetos k-finitos y decidibilidad]]></article-title>
<article-title xml:lang="en"><![CDATA[K-finite objects and decidability]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Acuña Ortega]]></surname>
<given-names><![CDATA[Osvaldo]]></given-names>
</name>
<xref ref-type="aff" rid="A01"/>
</contrib>
</contrib-group>
<aff id="A01">
<institution><![CDATA[,Universidad de Costa Rica Escuela de Matemática CIMPA]]></institution>
<addr-line><![CDATA[ San José]]></addr-line>
<country>Costa Rica</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2014</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2014</year>
</pub-date>
<volume>21</volume>
<numero>1</numero>
<fpage>1</fpage>
<lpage>10</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S1409-24332014000100001&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S1409-24332014000100001&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S1409-24332014000100001&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[We study the k-finite and decidable objects in an elementary topos. We prove some results concerning k-finite and decidable objects.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Se estudian los conceptos de objetos k-finitos y el concepto de objeto decidible en un topos elemental. Se prueban algunos resultados sobre objetos k-finitos y objetos decidibles.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Topoi]]></kwd>
<kwd lng="en"><![CDATA[k-finite objects]]></kwd>
<kwd lng="en"><![CDATA[decidability]]></kwd>
<kwd lng="es"><![CDATA[Topos]]></kwd>
<kwd lng="es"><![CDATA[objetos k-finitos]]></kwd>
<kwd lng="es"><![CDATA[decidibilidad]]></kwd>
</kwd-group>
</article-meta>
</front><body><![CDATA[ <div style="text-align: justify;">     <div style="text-align: center;"><font  style="font-family: Verdana; font-weight: bold;" size="4"> Objetos k-finitos y decidibilidad</font>    <br> </div> <font style="font-family: Verdana;" size="2"></font>    <br>     <div style="text-align: center;"><font  style="font-family: Verdana; font-weight: bold;" size="4">K-finite objects and decidability</font>    <br> </div> <font style="font-family: Verdana;" size="2"></font>    <br>     <div style="text-align: center;"><font style="font-family: Verdana;"  size="2">Osvaldo Acu&ntilde;a Ortega</font><sup><small><span  style="font-family: Verdana;"><a href="#1">*</a><a name="2"></a>*</span></small></sup>    <br> </div> <font style="font-family: Verdana;" size="2"></font>    <br> <small><span style="font-family: Verdana;"><a name="Correspondencia2"></a>*<a  href="#Correspondencia1">Direcci&oacute;n para correspondencia</a></span></small><a  href="#Correspondencia1">:</a>    ]]></body>
<body><![CDATA[<br> <hr style="width: 100%; height: 2px;"><font  style="font-family: Verdana;" size="2"></font><font  style="font-family: Verdana; font-weight: bold;" size="3">Abstract</font>    <br> <font style="font-family: Verdana;" size="2">We study the k-finite and decidable objects in an elementary topos. We prove some results concerning k-finite and decidable objects.</font>    <br> <font style="font-family: Verdana;" size="2"></font>    <br> <font style="font-family: Verdana;" size="2"><span  style="font-weight: bold;">Keywords</span>: Topoi, k-finite objects, decidability.</font>    <br> <font style="font-family: Verdana;" size="2"></font>    <br> <font style="font-family: Verdana; font-weight: bold;" size="3">Resumen</font>    <br> <font style="font-family: Verdana;" size="2"></font>    <br> <font style="font-family: Verdana;" size="2">Se estudian los conceptos de objetos k-finitos y el concepto de objeto decidible en un topos elemental. Se prueban algunos resultados sobre objetos k-finitos y objetos decidibles.</font>    <br> <font style="font-family: Verdana;" size="2"></font>    <br> <font style="font-family: Verdana;" size="2"><span  style="font-weight: bold;">Palabras clave</span>: Topos, objetos k-finitos, decidibilidad.</font>    ]]></body>
<body><![CDATA[<br> <font style="font-family: Verdana;" size="2"></font>    <br> <font style="font-family: Verdana;" size="2"><span  style="font-weight: bold;">Mathematics Subject Classification:</span> 03G30, 18B25.</font>    <br> <hr style="width: 100%; height: 2px;"><font  style="font-family: Verdana;" size="2"></font>    <br> <font style="font-family: Verdana;" size="3"><font size="-1">Ver contenido disponible en pdf</font></font>    <br>     <br> <hr style="width: 100%; height: 2px;"><font  style="font-family: Verdana; font-weight: bold;" size="3">Referencias</font>    <br> <font style="font-family: Verdana;" size="2"></font>    <!-- ref --><br> <font style="font-family: Verdana;" size="2">[1] Acu&ntilde;a&#8211;Ortega, O. (1977) <span style="font-style: italic;">Finiteness in Topoi</span>. Ph. D. Dissertation, Wesleyan University,Middletown, CT.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=1949591&pid=S1409-2433201400010000100001&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font>    <br> <font style="font-family: Verdana;" size="2"></font>    ]]></body>
<body><![CDATA[<!-- ref --><br> <font style="font-family: Verdana;" size="2">[2] Acu&ntilde;a&#8211;Ortega, O.; Linton, F.E.J. (1979) &#8220;Finiteness and decidability I&#8221;, in: <span style="font-style: italic;">Applications of Sheaves</span>, Lecture Notes inMathematics 753, Springer&#8211;Verlag, New York: 80&#8211;100.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=1949594&pid=S1409-2433201400010000100002&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font>    <br> <font style="font-family: Verdana;" size="2"></font>    <!-- ref --><br> <font style="font-family: Verdana;" size="2">[3] Acu&ntilde;a&#8211;Ortega, O. (2011) &#8220;Una nota sobre objetos k-finitos en un topos Booleano con el objeto de los n&uacute;meros naturales&#8221;, <span  style="font-style: italic;">Revista de Matem&aacute;tica: Teor&iacute;a y Aplicaciones</span> 19(2): 239&#8211;245.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=1949597&pid=S1409-2433201400010000100003&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font>    <br> <font style="font-family: Verdana;" size="2"></font>    <!-- ref --><br> <font style="font-family: Verdana;" size="2">[4] Acu&ntilde;a&#8211;Ortega, O. (2013) &#8220;Sobre una construcci&oacute;n de unmonoide libre con identidad sobre un topos <span style="font-style: italic;">E</span> con el objeto de los n&uacute;meros naturales&#8221;, <span style="font-style: italic;">Revista de Matem&aacute;tica: Teor&iacute;a y Aplicaciones</span> 20(1): 79&#8211;94.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=1949600&pid=S1409-2433201400010000100004&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font>    <br> <font style="font-family: Verdana;" size="2"></font>    <!-- ref --><br> <font style="font-family: Verdana;" size="2">[5] Kock, A.; Lecouturier, P.; Mikkelsen, Ch.J. (1975) &#8220;Some topos theoretic concepts of finiteness&#8221;, in: <span  style="font-style: italic;">Model Theory and Topoi</span>, Lecture Notes in Mathematics 445, Springer&#8211;Verlag, New York: 209&#8211;283.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=1949603&pid=S1409-2433201400010000100005&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font>    <br>     <br> <small><span style="font-family: Verdana;"><a name="Correspondencia1"></a><a  href="#Correspondencia2">*</a>Correspondencia a:</span></small>    <br> <font style="font-family: Verdana;" size="2">Osvaldo Acu&ntilde;a Ortega</font><small><span  style="font-family: Verdana;"></span></small><font  style="font-family: Verdana;" size="2">: CIMPA &amp; Escuela de Matem&aacute;tica, Universidad de Costa Rica, San Jos&eacute;,Costa Rica.</font>    <br> <font style="font-family: Verdana;" size="2"><a name="1"></a><a  href="#Correspondencia2">*</a>CIMPA &amp; Escuela de Matem&aacute;tica, Universidad de Costa Rica, San Jos&eacute;,Costa Rica.</font>    <br> <hr style="width: 100%; height: 2px;"><font  style="font-family: Verdana;" size="2"></font>     <div style="text-align: center;"><font  style="font-family: Verdana; font-weight: bold;" size="2">Received: 06/Aug/2013; Revised: 25/Oct/2013; Accepted: 30/Oct/2013</font><font  style="font-family: Verdana;" size="2"></font></div> </div>      ]]></body><back>
<ref-list>
<ref id="B1">
<label>1</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Acuña-Ortega]]></surname>
<given-names><![CDATA[O.]]></given-names>
</name>
</person-group>
<source><![CDATA[Finiteness in Topoi]]></source>
<year>1977</year>
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<label>2</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Acuña-Ortega]]></surname>
<given-names><![CDATA[O]]></given-names>
</name>
<name>
<surname><![CDATA[Linton]]></surname>
<given-names><![CDATA[F.E.J.]]></given-names>
</name>
</person-group>
<article-title xml:lang="en"><![CDATA[“Finiteness and decidability I”]]></article-title>
<source><![CDATA[Applications of Sheaves: Lecture Notes in Mathematics 753]]></source>
<year>1979</year>
<page-range>80-100</page-range><publisher-loc><![CDATA[^eNew York New York]]></publisher-loc>
<publisher-name><![CDATA[Springer-Verlag]]></publisher-name>
</nlm-citation>
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</person-group>
<article-title xml:lang="es"><![CDATA[Una nota sobre objetos k-finitos en un topos Booleano con el objeto de los números naturales]]></article-title>
<source><![CDATA[Revista de Matemática: Teoría y Aplicaciones]]></source>
<year>2011</year>
<volume>19</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>239-245.</page-range></nlm-citation>
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<given-names><![CDATA[O.]]></given-names>
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<article-title xml:lang="es"><![CDATA[Sobre una construcción de unmonoide libre con identidad sobre un topos E con el objeto de los números naturales]]></article-title>
<source><![CDATA[Revista de Matemática: Teoría y Aplicaciones]]></source>
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<person-group person-group-type="author">
<name>
<surname><![CDATA[Kock]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Lecouturier]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Mikkelsen]]></surname>
<given-names><![CDATA[Ch.J.]]></given-names>
</name>
</person-group>
<article-title xml:lang="en"><![CDATA[Some topos theoretic concepts of finiteness]]></article-title>
<source><![CDATA[Model Theory and Topoi: Lecture Notes in Mathematics 445]]></source>
<year>1975</year>
<page-range>209-283.</page-range><publisher-loc><![CDATA[^eNew York New York]]></publisher-loc>
<publisher-name><![CDATA[Springer-Verlag]]></publisher-name>
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</back>
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