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Expanding the additive reduct of a model of Peano arithmetic
Author(s) -
Murakami Masahiko,
Tsuboi Akito
Publication year - 2003
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.200310038
Subject(s) - peano axioms , reduct , mathematics , multiplication (music) , second order arithmetic , arithmetic , discrete mathematics , combinatorics , rough set , data mining , computer science
Let M be a model of first order Peano arithmetic ( PA ) and I an initial segment of M that is closed under multiplication. Let M 0 be the {0, 1,+}‐reduct of M . We show that there is another model N of PA that is also an expansion of M 0 such that a · M a = a · N a if and only if a ∈ I for all a ∈ M .