M. Golshani

activity

19952026

H O D

9 citations · 34 across the 60 of their papers we have counts for

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Showing 2015Show all

18 papers · 1 filter

math.LO2015

HOD, V and the GCH

Mohammad Golshani

Starting from large cardinals we construct a model of $Z F C$ in which the $GC H$ fails everywhere, but such that $GC H$ holds in its $H O D$ . The result answers a question of Sy Friedma…

math.LO2015

The tree property on a countable segment of successors of singular cardinals

Mohammad Golshani, Yair Hayut

Starting from the existence of many supercompact cardinals, we construct a model of ZFC in which the tree property holds at a countable segment of successor of singular cardinals.

math.LO2015

Killing GCH everywhere by a cofinality-preserving forcing notion over a model of GCH

Sy David Friedman, Mohammad Golshani

Starting from large cardinals we construct a pair $V_{1} \subseteq V_{2}$ of models of $Z F C$ with the same cardinals and cofinalities such that $GC H$ holds in $V_{1}$ and fails everywhere…

math.LO2015

Shelah's strong covering property and CH in V[r]

Esfandiar Eslami, Mohammad Golshani

In this paper we review Shelah's strong covering property and its applications. We also extend some of the results of Shelah and Woodin on the failure of $C H$ by adding a real.

math.LO2015

Killing the GCH everywhere with a single real

Sy David Friedman, Mohammad Golshani

Shelah-Woodin investigate the possibility of violating instances of $GC H$ through the addition of a single real. In particular they show that it is possible to obtain a failure of…

math.LO2015

Independence of higher Kurepa hypotheses

Sy David Friedman, Mohammad Golshani

We study the Generalized Kurepa Hypothesis introduced by Chang. We show that relative to the existence of an inaccessible cardinal the Gap- $n$ -Kurepa hypothesis does not follow fro…

math.LO2015

More on almost Souslin Kurepa trees

Mohammad Golshani

It is consistent that there exists a Souslin tree $T$ such that after forcing with it, $T$ becomes an almost Souslin Kurepa tree. This answers a question of Zakrzewski.

math.LO2015

Almost Souslin Kurepa trees

Mohammad Golshani

We show that the existence of an almost Souslin Kurepa tree is consistent with $Z F C$ . We also prove their existence in $L$ . These results answer two questions from Zakrzewski.

math.LO2015

On cuts in ultraproducts of linear orders I

Mohammad Golshani, Saharon Shelah

For an ultrafilter $D$ on a cardinal $κ,$ we wonder for which pair $(θ_{1}, θ_{2})$ of regular cardinals, we have: for any $(θ_{1} + θ_{2})^{+} -$ saturated dense linear order $J, J^{κ} / D$ has a…

math.LO2015★ 1 cited

Singular cofinality conjecture and a question of Gorelic

Mohammad Golshani

We give an affirmative answer to a question of Gorelic \cite{Gorelic}, by showing it is consistent, relative to the existence of large cardinals, that there is a proper class of ca…

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…

math.LO2015

An introdution to forcing

Mohammad Golshani

The aim of these lectures is to give a short introduction to forcing. We will avoid metamathematical issues as much as possible and similarly we will avoid performing the actual co…

math.LO2015

Adding a lot of Cohen reals by adding a few II

Moti Gitik, Mohammad Golshani

We study pairs $(V, V_{1})$ , $V \subseteq V_{1}$ , of models of $Z F C$ such that adding $κ -$ many Cohen reals over $V_{1}$ adds $λ -$ many Cohen reals over $V$ for some $λ > κ$ .

math.LO2015

Adding a lot of Cohen reals by adding a few I

Moti Gitik, Mohammad Golshani

In this paper we produce models $V_{1} \subseteq V_{2}$ of set theory such that adding $κ$ -many Cohen reals to $V_{2}$ adds $λ$ -many Cohen reals to $V_{1}$ , for some $λ > κ$ . We deal mainly w…

math.LO2015

On Foreman's maximality principle

Mohammad Golshani, Yair Hayut

In this paper we consider the Foreman's maximality principle, which says that any non-trivial forcing notion either adds a new real or collapses some cardinals. We prove the consis…

math.LO2015

On the notion of generic cut for models of ZFC

Mohammad Golshani

We define the notion of generic cut between models of ZFC and give some examples.

math.LO2015★ 1 cited

On the notions of dimension and transcendence degree for models of ZFC

Mohammad Golshani

We define notions of generic dimension and generic transcendence degree between models of ZFC and give some examples.

math.LO2015★ 2 cited

Woodin's surgery method

Mohammad Golshani

In this short paper we give an overview of Woodin's surgery method.