A. Valizadeh

works on

beatty sequences 1 elementary number theory 1 irrational numbers 1 iterated sequences 1 membership criteria 1

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math.LO2025

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…

math.LO2025

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 $⟨ Z, <, +, f, 0 ⟩$ where $f$ is the function that maps each $x$ to the integer part of $…

math.LO2024

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 $Z_{I^} \pm = (Z, +, 0, 1, f)$ where $f : x \to ⌊ I^\pm x ⌋$ is a unary function with $I^\pm$ a fixed…