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Convergence Laws for Very Sparse Random Structures with Generalized Quantifiers
Author(s) -
Kaila Risto
Publication year - 2002
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/1521-3870(200202)48:2<301::aid-malq301>3.0.co;2-z
Subject(s) - mathematics , probabilistic logic , convergence (economics) , law of large numbers , convergence of random variables , calculus (dental) , discrete mathematics , random variable , statistics , medicine , dentistry , economics , economic growth
We prove convergence laws for logics of the form $ {\cal L} ^{\omega} _{\infty \omega} (\cal Q) $ , where $ {\cal Q} $ is a properly chosen collection of generalized quantifiers, on very sparse finite random structures. We also study probabilistic collapsing of the logics $ {\cal L} ^{k} _{\infty \omega} (\cal Q) $ , where $ {\cal Q} $ is a collection of generalized quantifiers and k ∈ ℕ + , under arbitrary probability measures of finite structures.