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Mohammad Golshani

Publications and source records attributed to Mohammad Golshani.

83 records · Page 5Linked to original sources
arXiv2015

Killing the GCH everywhere with a single real

Shelah-Woodin investigate the possibility of violating instances of $GCH$ through the addition of a single real. In particular they show that it is possible to obtain a failure of $CH$ by adding a single real to a model of $GCH$, preserving cofinalities. In this article we strengthen their result by showing that it is possible to violate $GCH$ at all infinite cardinals by adding a single real to a model of $GCH.$ Our assumption is the existence of an $H(κ^{+3})$-strong cardinal, by work of Gitik and Mitchell it is known that more than an $H(κ^{++})$-strong cardinal is required.

math.LO↗
arXiv2015

Singular cofinality conjecture and a question of Gorelic

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 cardinals $α$ with $cf(α)=ω_1$ and $α^ω> α.$

math.LO↗
arXiv2015

An introdution to forcing

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 construction of forcing. We assume familiarity with basic predicate logic, the axioms of ZF C set theory and constructible sets. We will also make use of tools like the coding of Borel sets and the Shoenfield absoluteness result.

math.LO↗
arXiv2015

Adding a lot of Cohen reals by adding a few I

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 with the case when $V_1$ and $V_2$ have the same cardinals.

math.LO↗