7 papers
A Note on Iterated Beatty Sequences
Mohsen Khani, Ali N. Valizadeh, Afshin Zarei
For any irrational number and given a positive , we use elementary number theory to introduce a necessary and sufficient con…
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 $…
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 tra…
A Tame Generic Structure with Non-Algebraic Geometric Closure
Somaye Jalili, Massoud Pourmahdian, Ali N. Valizadeh
By providing a procedure to apply Hrushovski's amalgamation method to the setting of classes of infinite structures, we introduce the notion of \textit{paracollapsed} structures. W…
Strict Superstablity and Decidability of Certain Generic Graphs
Ali N. Valizadeh, Massoud Pourmahdian
We show that the Hrushovski-\fraisse limit of certain classes of trees lead to strictly superstable theories of various U-ranks. In fact, for each we int…
Pseudofiniteness in Hrushovski Constructions
Ali N. Valizadeh, Massoud Pourmahdian
In a relational language consisting of a single relation we investigate pseudofiniteness of certain Hrushovski constructions obtained via predimension functions. It is notab…