From the 1 of 4 linked papers with an AI index.
4 papers
A Note on Iterated Beatty Sequences
Mohsen Khani, Ali N. Valizadeh, Afshin Zarei
The paper provides an elementary number‑theoretic criterion that exactly characterizes when a natural number belongs to the nth iterate of a Beatty sequence with irrational modulus…
Fibonacci Numbers and Model-Complete Axiomatization of Presburger Arithmetic Expanded with a Beatty Sequence
Mohsen Khani, Ali N. Valizadeh, Afshin Zarei
We introduce a recursive theory that completely axiomatizes the structure where is the function that maps each to the integer part of $…
Construction of a valued field whose valuation ring is definable but neither nor -definable in the language of rings
Mohsen Khani, Shaghayegh Shirani, Zahra Yadegari +1
We give an example of a valued field such that the valuation ring is definable by an -formula without parameters, but there is no $\exists\forall\exist…
Model-completeness and decidability of the additive structure of integers expanded with a function for a Beatty sequence
Mohsen Khani, Ali N. Valizadeh, Afshin Zarei
We introduce a model-complete theory which completely axiomatizes the structure where is a unary function with a fixed…