On a question of Phillips

WOS: A1997WG83000009In [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 alpha-dimensional vector space over Q when alpha 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