Mostafa Mirabi

activity

20162026

most citedForcing with Invariant Measures

1 citations · 1 across the 17 of their papers we have counts for

collaborators

19 papers

math.LO2026

Almost-linear Zarankiewicz bounds in $1$ -semi-equational theories

Hongyi Gou, Mostafa Mirabi, Mihir Mittal +2

We study multipartite hypergraphs definable in $1$ -semi-equational theories and prove almost-linear Zarankiewicz bounds in every fixed arity $r \geq 2$ . If $T$ is a $1$ -semi-equation…

math.CO2026

Resilient forest universality in percolated dense graphs

Mostafa Mirabi

Christoph, Müyesser and Wigderson recently asked whether an approximate form of the Erdős-Sós conjecture is robust under random edge deletions. We establish a density-sensitive tra…

math.PR2026

First-Order Laws for Random Geometric Graphs on the Torus

Simi Haber, Mostafa Mirabi, Saharon Shelah

Let $G_{D} (n; r)$ be the random geometric graph generated by $n$ independent uniform points on the $D$ -dimensional torus, with adjacency defined by torus $L^{\infty}$ -distance at most $…

math.CO2026

One-point extensions of Euclidean Ramsey sets

Mostafa Mirabi

Let $X$ be a finite Euclidean Ramsey set. We prove that adjoining any point outside the affine hull of $X$ gives another Euclidean Ramsey set, answering a conjecture of Ivan, Leade…

math.LO2026

Canonical expansions of $R_{Q}$ -germs

Mostafa Mirabi

Let $H_{Q}$ be the field of unary germs at $0^{+}$ definable in the quasianalytic o-minimal structure $R_{Q}$ of Kaiser-Rolin-Speissegger. We c…

math.LO2026

Limit laws for component-pruned sparse random graphs and percolated tori

Mostafa Mirabi, Saharon Shelah

We prove an $MSO_{2}$ zero-one law for a very sparse Erdős-Rényi graph after pruning by component order. Let $p_{n} = c_{n} / n$ , where $c_{n} \to 0$ , and delete every component of orde…

math.LO2026

The failure of stable composition for equivalence relations in simple theories

Mostafa Mirabi

Casanovas and Potier proved that algebraic quantification preserves stability of formulas. They also gave a nonsimple example, answering a question of Laskowski, showing that the a…

math.NT2026

Level totients for integer mosaics

The Anh Dao, Tim Kasian, Mostafa Mirabi

We study a level analog of Euler's totient function for integer mosaics. Let $P_{i} (n)$ be the set of primes appearing in the first $i$ levels of the mosaic of $n$ , and let $φ_{i} (n)$ …

math.LO2026★ 1 cited

Forcing with Invariant Measures

Nathanael Ackerman, Cameron Freer, Mohammad Golshani +2

This paper introduces a model-theoretic generalization of the notion of forcing with random reals, in which forcing gives rise to random generic structures. Specifically, we consid…

math.LO2026

On the computability of cofinal Fraïssé limits

Nathanael Ackerman, Cameron Freer, Mostafa Mirabi

For any collection of finite structures closed under isomorphism (i.e., an age) which has the Hereditary Property (HP), the Joint Embedding Property (JEP), and the Cofinal Amalgama…

math.CO2025

Structured Sunflowers

Nathanael Ackerman, Mary Leah Karker, Mostafa Mirabi

We call an infinite structure $M$ sunflowerable if whenever $M^{'}$ is isomorphic to $M$ with underlying set $M^{'}$ , consisting of finite sets of bounded s…

math.CO2025

Rainbow Threshold Graphs

Nathanael Ackerman, Mostafa Mirabi

We define a generalization of threshold graphs which we call $k$ -rainbow threshold graphs. We show that the collection of $k$ -rainbow threshold graphs do not satisfy the $0$ - $1$ la…

math.GN2025

Absoluteness of Fixed Points

Nathanael Ackerman, Mostafa Mirabi

We characterize those complete commutative positive linear ordered monoids $W$ such that whenever $f$ is a map from a Cauchy complete $W$ -metric space to itself, the existence of a…

math.LO2023

Computability of Countable Sunflowers

Nathanael Ackerman, Leah Karker, Mostafa Mirabi

We provide a characterization of when a countably infinite set of finite sets contains an infinite sunflower. We also show that the collection of such sets is Turing equivalent to…

math.CO2023

Algebraic Sunflowers

Nathanael Ackerman, Mostafa Mirabi

We study sunflowers within the context of finitely generated substructures of ultrahomogeneous structures. In particular, we look at bounds on how large a set system is needed to g…

math.LO2023

Asymptotic Classes of Trees and $ℵ_{0}$ -categoricity

Mostafa Mirabi

This paper focuses on the characterization of $ℵ_{0}$ -categorical theories of trees in the following sense: for any $ℵ_{0}$ -cateorical theory $T$ of trees there is a tree pla…

math.LO2021

MS-measurability via coordinatization

Mostafa Mirabi

We study $M S$ -measurability of structures obtained as expansions of finite-height trees. We show that an admissible nil-interaction coordinatized structure is $M S$ -measurable whene…

math.CO2021

From Shelah's block-content to Hales-Jewett

Mohammad Golshani, Mostafa Mirabi, Saharon Shelah

We study the quantitative relationship between the Hales-Jewett numbers and Shelah's block-content canonization functions. Block-content canonization yields a block subspace on whi…

math.LO2016

Definable tree property for uncountable regular cardinals

Mohammad Golshani, Mostafa Mirabi

The primary goal of this paper is to establish a model of $Z F C$ wherein the definable tree property is affirmed for all uncountable regular cardinals. This endeavor commences with…

Almost-linear Zarankiewicz bounds in 1-semi-equational theories

Resilient forest universality in percolated dense graphs

First-Order Laws for Random Geometric Graphs on the Torus

One-point extensions of Euclidean Ramsey sets

Canonical expansions of RQ​-germs

Limit laws for component-pruned sparse random graphs and percolated tori

The failure of stable composition for equivalence relations in simple theories

Level totients for integer mosaics

Forcing with Invariant Measures

On the computability of cofinal Fraïssé limits

Structured Sunflowers

Rainbow Threshold Graphs

Absoluteness of Fixed Points

Computability of Countable Sunflowers

Algebraic Sunflowers

Asymptotic Classes of Trees and ℵ0​-categoricity

MS-measurability via coordinatization

From Shelah's block-content to Hales-Jewett

Definable tree property for uncountable regular cardinals

Almost-linear Zarankiewicz bounds in $1$ -semi-equational theories

Canonical expansions of $R_{Q}$ -germs

Asymptotic Classes of Trees and $ℵ_{0}$ -categoricity