M. Khani

works on

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

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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.LO2025

Construction of a valued field whose valuation ring is definable but neither $\exists\forall\exists$ nor $\forall\exists\forall$ -definable in the language of rings

Mohsen Khani, Shaghayegh Shirani, Zahra Yadegari +1

We give an example of a valued field $(K, A)$ such that the valuation ring $A$ is definable by an $L_{ring}$ -formula without parameters, but there is no $\exists\forall\exist…

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…

Fibonacci Numbers and Model-Complete Axiomatization of Presburger Arithmetic Expanded with a Beatty Sequence

Construction of a valued field whose valuation ring is definable but neither ∃∀∃ nor ∀∃∀-definable in the language of rings

Model-completeness and decidability of the additive structure of integers expanded with a function for a Beatty sequence

Construction of a valued field whose valuation ring is definable but neither $\exists\forall\exists$ nor $\forall\exists\forall$ -definable in the language of rings