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An Independence Result on Weak Second Order Bounded Arithmetic
Author(s) -
Kuroda Satoru
Publication year - 2001
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(200105)47:2<183::aid-malq183>3.0.co;2-z
Subject(s) - corollary , mathematics , bounded function , order (exchange) , second order arithmetic , division (mathematics) , arithmetic , independence (probability theory) , function (biology) , discrete mathematics , mathematical analysis , statistics , peano axioms , finance , evolutionary biology , economics , biology
We show that length initial submodels of S 1 2 can be extended to a model of weak second order arithmetic. As a corollary we show that the theory of length induction for polynomially bounded second order existential formulae cannot define the function division.