Abstract
Many modern models of informational defence represents by graphs and partial orders (posets). It is very important to resolve such algorithmic problems as searching of elements that satisfies some conditions (or, another words, to resolve recognition problems) in this models. Algebraic geometry is resolving such problems and searches elements that is solution of system of equations. But systems could be infinite. In this article we’re formulating the condition for poset that every infinite system under such posets can be reduce to finite system and still be equivalent to origin system.
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