The Skolem-Bang Theorems in Ordered Fields with an $IP$

Details The Skolem-Bang Theorems in Ordered Fields with an $IP$ The Skolem-Bang Theorems in Ordered Fields with an $IP$

2007-05-23

arxiv.org/abs/0705.3356v1

Mathematics

Logic

28 pages

Scientific paper

This paper is concerned with the extent to which the Skolem-Bang theorems in Diophantine approximations generalise from the standard setting of $$ to structures of the form $$, where $F$ is an ordered field and $I$ is an integer part of $F$. We show that some of these theorems are hold unconditionally in general case (ordered fields with an integer part). The remainder results are based on Dirichlet's and Kronecker's theorems. Finally we extend Dirichlet's theorem to ordered fields with $IE_1$ integer part.

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