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On a Question of Phillips
Author(s) -
Gencer Çiǧdem,
Terziler Mehmet
Publication year - 1997
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.19970430110
Subject(s) - mathematics , cardinality (data modeling) , connection (principal bundle) , linear space , space (punctuation) , pure mathematics , vector space , function (biology) , combinatorics , discrete mathematics , geometry , computer science , evolutionary biology , biology , data mining , operating system
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.