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

Saharon Shelah. "Zero-one laws for graphs with edge probabilities decaying with distance. Part II." Fundamenta Mathematicae 185.3 (2005): 211-245. <http://eudml.org/doc/283301>.

@article{SaharonShelah2005,
abstract = {Let Gₙ be the random graph on [n] = 1,...,n with the probability of i,j being an edge decaying as a power of the distance, specifically the probability being $p_\{|i-j|\} = 1/|i-j|^\{α\}$, where the constant α ∈ (0,1) is irrational. We analyze this theory using an appropriate weight function on a pair (A,B) of graphs and using an equivalence relation on B∖A. We then investigate the model theory of this theory, including a “finite compactness”. Lastly, as a consequence, we prove that the zero-one law (for first order logic) holds.},
author = {Saharon Shelah},
journal = {Fundamenta Mathematicae},
keywords = {random graph; weight function; finite compactness; zero-one law},
language = {eng},
number = {3},
pages = {211-245},
title = {Zero-one laws for graphs with edge probabilities decaying with distance. Part II},
url = {http://eudml.org/doc/283301},
volume = {185},
year = {2005},
}

TY - JOUR
AU - Saharon Shelah
TI - Zero-one laws for graphs with edge probabilities decaying with distance. Part II
JO - Fundamenta Mathematicae
PY - 2005
VL - 185
IS - 3
SP - 211
EP - 245
AB - Let Gₙ be the random graph on [n] = 1,...,n with the probability of i,j being an edge decaying as a power of the distance, specifically the probability being $p_{|i-j|} = 1/|i-j|^{α}$, where the constant α ∈ (0,1) is irrational. We analyze this theory using an appropriate weight function on a pair (A,B) of graphs and using an equivalence relation on B∖A. We then investigate the model theory of this theory, including a “finite compactness”. Lastly, as a consequence, we prove that the zero-one law (for first order logic) holds.
LA - eng
KW - random graph; weight function; finite compactness; zero-one law
UR - http://eudml.org/doc/283301
ER -