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arXiv · 2311.11168

Bounded quantifier depth spectrum for random uniform hypegraphs

Svetlana Popova
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Abstract

The notion of spectrum for first-order properties introduced by J. Spencer for Erdos-Renyi random graph is considered in relation to random uniform hypergraphs. In this work we study the set of limit points of the spectrum for first-order formulae with bounded quantifier depth and obtain bounds for its maximum value. Moreover, we prove zero-one k-laws for the random uniform hypergraph and improve the bounds for the maximum value of the spectrum for first-order formulae with bounded quantifier depth. We obtain that the maximum value of the spectrum belongs to some two-element set.

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Svetlana Popova. 2023-11-18. Bounded quantifier depth spectrum for random uniform hypegraphs. https://arxiv.org/abs/2311.11168

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