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A Model‐Theoretic Property of Sharply Bounded Formulae, with some Applications
Author(s) -
Johannsen Jan
Publication year - 1998
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/malq.19980440207
Subject(s) - mathematics , bounded function , property (philosophy) , independence (probability theory) , discrete mathematics , pure mathematics , mathematical analysis , statistics , philosophy , epistemology
Abstract We define a property of substructures of models of arithmetic, that of being length‐initial, and show that sharply bounded formulae are absolute between a model and its length‐initial submodels. We use this to prove independence results for some weak fragments of bounded arithmetic by constructing appropriate models as length‐initial submodels of some given model.