Hierarchy (mathematics)

<h2 id="related-terminology">Related terminology</h2>
<p>Individual elements of a hierarchy are often called levels and a hierarchy is said to be infinite if it has infinitely many distinct levels but said to collapse if it has only finitely many distinct levels.
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<h2 id="example">Example</h2>
<p>In <a href="/facts/Theoretical_computer_science/jSkGGuvy">theoretical computer science</a>, the <a href="/facts/Time_hierarchy/sm75DR1s">time hierarchy</a> is a classification of <a href="/facts/Decision_problem/cQNWjbdE">decision problems</a> according to the amount of time required to solve them.
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<h2 id="see-also">See also</h2>

<ul><li><a href="/facts/Order_theory/gn6fM3oJ">Order theory</a></li>
<li><a href="/facts/Nested_set_collection/o5f1ujSn">Nested set collection</a></li>
<li><a href="/facts/Lattice_(disambiguation)/uU9oQkyj">Lattice</a></li></ul>
<p>Tree related topics:
</p>
<ul><li><a href="/facts/Tree_structure/R2vT5UIu">Tree structure</a></li>
<li><a href="/facts/Tree_(data_structure)/RcXz9noF">Tree (data structure)</a></li>
<li><a href="/facts/Tree_(graph_theory)/TCWk4Joy">Tree (graph theory)</a></li>
<li><a href="/facts/Tree_network/bJQpQPQC">Tree network</a></li>
<li><a href="/facts/Tree_(descriptive_set_theory)/RqSGQaRG">Tree (descriptive set theory)</a></li>
<li><a href="/facts/Tree_(set_theory)/5zkqfoz3">Tree (set theory)</a></li></ul>
<p><a href="/facts/Computably_enumerable_set/lpzr8jHn">Effective complexity</a> hierarchies:
</p>
<ul><li><a href="/facts/Polynomial_hierarchy/73N468Dv">Polynomial hierarchy</a></li>
<li><a href="/facts/Exponential_hierarchy/BlrcTxfS">Exponential hierarchy</a></li>
<li><a href="/facts/Chomsky_hierarchy/tUYCL00R">Chomsky hierarchy</a></li></ul>
<p>Ineffective complexity hierarchies:
</p>
<ul><li><a href="/facts/Arithmetical_hierarchy/rQptcBFK">Arithmetical hierarchy</a></li>
<li><a href="/facts/Hyperarithmetical_hierarchy/3tGU6KR1">Hyperarithmetical hierarchy</a></li>
<li><a href="/facts/Analytical_hierarchy/C9r61LzA">Analytical hierarchy</a></li></ul>
<p>In set theory or logic:
</p>
<ul><li><a href="/facts/Borel_hierarchy/u15QcVmv">Borel hierarchy</a></li>
<li><a href="/facts/Difference_hierarchy/ay3nmSt6">Difference hierarchy</a></li>
<li><a href="/facts/Wadge_hierarchy/N0nqDjbg">Wadge hierarchy</a></li>
<li><a href="/facts/Abstract_algebraic_hierarchy/PcpP38IA">Abstract algebraic hierarchy</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>We may need a bigger topos. <a href="/wiki/Topos" target="_blank">/wiki/Topos</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
</ol>

Hierarchy (mathematics) open-in-new

Hierarchy (mathematics)