R. Mohammadpour

activity

20152026

collaborators

12 papers

math.LO2026

A Note on a Theorem of Apter

Rahman Mohammadpour, Otto Rajala, Sebastiano Thei

We show that the consistency of $ZF + AD_{R} + ‘‘Θ$ is measurable $"$ implies the consistency of $ZF + ‘‘Θ$ is the least strongly regular cardinal…

math.LO2026

Todorcevic's Problem on Rado's Conjecture

Monroe Eskew, Rahman Mohammadpour

In his Mostowski lecture in Wrocław in 2024, Stevo Todorčević asked whether it is consistent that Rado's Conjecture holds at two successive cardinals. We show that it is consistent…

math.LO2024

Martin's Axiom and Weak Kurepa Hypothesis

Rahman Mohammadpour

I show that it is consistent relative to the consistency of a Mahlo cardinal that Martin's axiom holds at $ω_{2}$ , but the weak Kurepa Hypothesis fails. This answers a question posed…

math.LO2023

On Indestructible Strongly Guessing Models

Rahman Mohammadpour, Boban Velickovic

In \cite{MV} we defined and proved the consistency of the principle $GM^{+} (ω_{3}, ω_{1})$ which implies that many consequences of strong forcing axioms hold simultaneously at $ω_{2}$ …

math.LO2022

A Road To Compactness Through Guessing Models

Rahman Mohammadpour

The compactness phenomenon is one of the featured aspects of structuralism in mathematics. In simple and broad words, a compactness property holds in a structure if a related prope…

math.LO2022

Specialising Trees With Small Approximations II

Rahman Mohammadpour

We show that the existence of a well-known type of ideals on a regular cardinal $λ$ implies a compactness property concerning the specialisability of a tree of height $λ$ with no c…

math.LO2022

Indestructible Guessing Models And The Approximation Property

Rahman Mohammadpour

In this short note, we shall prove some observations regarding the connection between indestructible $ω_{1}$ -guessing models and the $ω_{1}$ -approximation property of forcing notions.

math.LO2020

Almost Strong Properness

Rahman Mohammadpour

We introduce the forcing property "almost strong properness" which sits between properness and strong properness. As an application, we introduce a simple forcing with finite condi…

math.LO2018

Guessing models and the approachability ideal

Rahman Mohammadpour, Boban Velickovic

Starting with two supercompact cardinals we produce a generic extension of the universe in which a principle that we call $GM^{+} (ω_{3}, ω_{1})$ holds. This principle implies ${\rm…

math.LO2016

The tree property at double successors of singular cardinals of uncountable cofinality

Mohammad Golshani, Rahman Mohammadpour

Assuming the existence of a strong cardinal $κ$ and a measurable cardinal above it, we force a generic extension in which $κ$ is a singular strong limit cardinal of any prescribed…

math.LO2015

A Mid Version of Hamkins' Maximality Principle

Rahman Mohammadpour

We present new, streamlined proofs of certain maximality principles studied by Hamkins and Woodin. Moreover, we formulate an intermediate maximality principle, which is shown here…

math.LO2015

Cardinal collapsing and product forcing

Mohammad Golshani, Rahman Mohammadpour

Suppose $κ$ is a singular strong limit cardinal of countable cofinality and let $⟨ κ_{n} : n < ω ⟩$ be an incrasing sequence of regular cardinals cofinal in $κ$ . We show th…