On a Question of Phillips

Mathematical Logic Quarterly 43 (1):78-82 (1997)
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Abstract

In [5] Phillips proved that one can obtain the additive group of any nonstandard model *ℤ of the ring ℤ of integers by using a linear mod 1 function h : F ℚ, where F is the α-dimensional vector space over ℚ when α is the cardinality of *ℤ. In this connection it arises the question whether there are linear mod 1 functions which are neither addition nor quasi-linear. We prove that this is the case

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References found in this work

On non-standard models for number theory.Elliott Mendelson - 1961 - In Bar-Hillel, Yehoshua & [From Old Catalog] (eds.), Essays on the Foundations of Mathematics. Jerusalem,: Magnes Press. pp. 259--268.

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