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 <title>Open Problem Garden - Blatter-Specker Theorem for ternary relations - Comments</title>
 <link>http://openproblemgarden.org/op/blatter_specker_theorem_for_ternary_relations</link>
 <description>Comments for &quot;Blatter-Specker Theorem for ternary relations&quot;</description>
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 <title>Blatter-Specker Theorem for ternary relations</title>
 <link>http://openproblemgarden.org/op/blatter_specker_theorem_for_ternary_relations</link>
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    Author(s):
        &lt;a href=&quot;/category/makowsky_janos_a&quot;&gt;Makowsky&lt;/a&gt;&amp;nbsp;&amp;nbsp;
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    Subject:
        &lt;a href=&quot;/category/logic&quot;&gt;Logic&lt;/a&gt; » &lt;a href=&quot;/category/finite_model_theory&quot;&gt;Finite Model Theory&lt;/a&gt;&amp;nbsp;&amp;nbsp;
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        &lt;p&gt;Let &lt;img class=&quot;teximage&quot; src=&quot;/files/tex/05d3558ef52267cc1af40e658352d98883668ee3.png&quot; alt=&quot;$ C $&quot; /&gt; be a class of finite relational structures. We denote by &lt;img class=&quot;teximage&quot; src=&quot;/files/tex/0424410bfa103527ea1bad45a617f3c858938218.png&quot; alt=&quot;$ f_C(n) $&quot; /&gt; the number of structures in &lt;img class=&quot;teximage&quot; src=&quot;/files/tex/05d3558ef52267cc1af40e658352d98883668ee3.png&quot; alt=&quot;$ C $&quot; /&gt; over the labeled set &lt;img class=&quot;teximage&quot; src=&quot;/files/tex/c7ddbea37c6a7d9aed7f4f036f82d07a79e8cb95.png&quot; alt=&quot;$ \{0, \dots, n-1 \} $&quot; /&gt;. For any class &lt;img class=&quot;teximage&quot; src=&quot;/files/tex/05d3558ef52267cc1af40e658352d98883668ee3.png&quot; alt=&quot;$ C $&quot; /&gt; definable in monadic second-order logic with unary and binary relation symbols, Specker and Blatter showed that, for every &lt;img class=&quot;teximage&quot; src=&quot;/files/tex/88a27613e47cbe6d1aec6dc4b342b3265e2670aa.png&quot; alt=&quot;$ m \in \mathbb{N} $&quot; /&gt;, the function &lt;img class=&quot;teximage&quot; src=&quot;/files/tex/0424410bfa103527ea1bad45a617f3c858938218.png&quot; alt=&quot;$ f_C(n) $&quot; /&gt; is ultimately periodic modulo &lt;img class=&quot;teximage&quot; src=&quot;/files/tex/ddaab6dc091926fb1da549195000491cefae85c1.png&quot; alt=&quot;$ m $&quot; /&gt;. &lt;/p&gt;
&lt;div class=&quot;envtheorem&quot;&gt;&lt;b&gt;Question&lt;/b&gt;&amp;nbsp;&amp;nbsp; Does the Blatter-Specker Theorem hold for ternary relations. &lt;/div&gt;

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&lt;/table&gt;</description>
 <category domain="http://openproblemgarden.org/category/makowsky_janos_a">Makowsky, Janos A.</category>
 <category domain="http://openproblemgarden.org/category/blatter_specker_theorem">Blatter-Specker Theorem</category>
 <category domain="http://openproblemgarden.org/category/fmt00_luminy">FMT00-Luminy</category>
 <category domain="http://openproblemgarden.org/category/logic">Logic</category>
 <category domain="http://openproblemgarden.org/category/finite_model_theory">Finite Model Theory</category>
 <comments>http://openproblemgarden.org/op/blatter_specker_theorem_for_ternary_relations#comment</comments>
 <pubDate>Fri, 18 May 2012 11:38:55 +0200</pubDate>
 <dc:creator>dberwanger</dc:creator>
 <guid isPermaLink="false">37444 at http://openproblemgarden.org</guid>
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