<?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>0034-7426</journal-id>
<journal-title><![CDATA[Revista Colombiana de Matemáticas]]></journal-title>
<abbrev-journal-title><![CDATA[Rev.colomb.mat.]]></abbrev-journal-title>
<issn>0034-7426</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional de Colombia y Sociedad Colombiana de Matemáticas]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0034-74262018000200131</article-id>
<article-id pub-id-type="doi">10.15446/recolma.v52n2.77153</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[A direct proof of a theorem of Jech and Shelah on PCF algebras]]></article-title>
<article-title xml:lang="es"><![CDATA[Una prueba directa de un teorema de Jech y Shelah sobre álgebras PCF]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Martínez]]></surname>
<given-names><![CDATA[Juan Carlos]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universitat de Barcelona Facultat de Matemàtiques i Informàtica ]]></institution>
<addr-line><![CDATA[Barcelona ]]></addr-line>
<country>Spain</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2018</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2018</year>
</pub-date>
<volume>52</volume>
<numero>2</numero>
<fpage>131</fpage>
<lpage>137</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0034-74262018000200131&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0034-74262018000200131&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0034-74262018000200131&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract By using an argument based on the structure of the locally compact scattered spaces, we prove in a direct way the following result shown by Jech and Shelah: there is a family {B&#945;: &#945; &lt; &#969;1} of subsets of &#969;1 such that the following conditions are satis&#64257;ed: (a) max B &#945; - &#945;, (b) if &#945; &#8712; B &#946; then B&#945; &#8838; B &#946;, (c) if &#948; &#8804; &#945; and &#948; is a limit ordinal then B&#945; &#8745; &#948; is not in the ideal generated by the sets B&#946;, &#946; &lt; &#945;, and by the bounded subsets of &#948;, (d) there is a partition {An: n &#8712; &#969;} of &#969;1 such that for every &#945; and every n, B &#945; &#8745; A n is &#64257;nite.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen Utilizando un argumento basado en la estructura de los espacios localmente compactos dispersos, demostramos de una manera directa el siguiente resultado de Jech y Shelah: existe una familia {B&#945;: &#945; &lt; &#969;1} de subconjuntos de &#969;1 que verifica las siguientes condiciones: (a) max B &#945; - &#945;, (b) si &#945; &#8712; B &#946; entonces B &#945; &#8838; B &#946;, (c) si &#948; &#8804; &#945; y &#948; es un ordinal límite, entonces B&#945; &#8745; &#948; no pertenece al ideal generado por los conjuntos B&#946;, &#946; &lt; &#945;, y por los subconjuntos acotados de &#948;, (d) existe una partición {An: n &#8712; &#969;} de &#969;1 tal que para todo &#945; y para todo n, B &#945; &#8745; An es &#64257;nito.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[PCF theory]]></kwd>
<kwd lng="en"><![CDATA[locally compact scattered space]]></kwd>
<kwd lng="es"><![CDATA[teoría PCF]]></kwd>
<kwd lng="es"><![CDATA[espacio localmente compacto disperso]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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