Zero-one laws for graphs with edge probabilities decaying with distance. Part I

Saharon Shelah

doi:10.4064/fm175-3-1

Zero-one laws for graphs with edge probabilities decaying with distance. Part I

Saharon Shelah^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

Let G_n be the random graph on [n] = {1,...,n} with the possible edge {i, j} having probability p_|i-j| = 1/|i-j|^αfor j ≠ i, i + 1, i - 1 with α ε (0,1) irrational. We prove that the zero-one law (for first order logic) holds.

Original language	English
Pages (from-to)	195-239
Number of pages	45
Journal	Fundamenta Mathematicae
Volume	175
Issue number	3
DOIs	https://doi.org/10.4064/fm175-3-1
State	Published - 2002

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abstract = "Let Gn be the random graph on [n] = \{1,...,n\} with the possible edge \{i, j\} having probability p|i-j| = 1/|i-j|αfor j ≠ i, i + 1, i - 1 with α ε (0,1) irrational. We prove that the zero-one law (for first order logic) holds.",

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AB - Let Gn be the random graph on [n] = {1,...,n} with the possible edge {i, j} having probability p|i-j| = 1/|i-j|αfor j ≠ i, i + 1, i - 1 with α ε (0,1) irrational. We prove that the zero-one law (for first order logic) holds.

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Zero-one laws for graphs with edge probabilities decaying with distance. Part I

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