Premium
Nonstandard Models for a Fragment of the Arithmetic and Their Decision Problem
Author(s) -
Garro Ibrahim
Publication year - 1987
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.19870330602
Subject(s) - fragment (logic) , citation , arithmetic , computer science , information retrieval , mathematics , library science , algorithm
M := {X I x E Z[[U]], z 2 o} , where 2 is the antilexicographical ordering in which the indeterminate u becomes infinitely small. (The variable x here also denotes elements of the model); the opera. tions +, are interpreted by the usual operations of addition and multiplication in z[[u]], sx and px are interpreted as x + 1 and x 1 respectively, o is the zero power series, and the operation x A y is defined by [r-y if x z y , otherwise. x’y=