Mohammad Golshani

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math.LO2026

A Set-Theoretic Translation of Modal Logic via Forcing

Somayeh Chopoghloo, Mohammad Golshani

We develop a set-theoretic translation of a normal modal extension $T_{m}$ of a recursively axiomatizable first-order theory $T$ . We first pass to the Henkin expansion of the underly…

math.LO2026

Representing a ring as the endomorphism ring of an abelian group

Mohsen Asgharzadeh, Mohammad Golshani, Saharon Shelah

We investigate Baer's realization problem for almost free abelian groups, focusing on the extent to which rings can be represented as endomorphism rings under strong freeness condi…

math.LO2026

Cohen Forcing with Fraïssé Classes Beyond $ℵ_{1}$

Mohammad Golshani

Kostana [5] asked for natural conditions on a class $K$ to ensure that forcing with finite members of $K$ on an underlying set $X$ is forcing equivalent to Cohe…

math.LO2026

Martin's axiom and $ω_{1}^{2} ⟶ (ω_{1}^{2}, 3)^{2}$

Mohammad Golshani

Starting with CH and Hajnal's coloring, we show that a standard finite-support iteration of $σ$ -centered forcing notions gives a model of $M A_{ω_{1}} (σ$ -centered$)+2^{\aleph_0}=\ale…

A Set-Theoretic Translation of Modal Logic via Forcing

Representing a ring as the endomorphism ring of an abelian group

Cohen Forcing with Fraïssé Classes Beyond ℵ1​

Martin's axiom and ω12​⟶(ω12​,3)2

Cohen Forcing with Fraïssé Classes Beyond $ℵ_{1}$

Martin's axiom and $ω_{1}^{2} ⟶ (ω_{1}^{2}, 3)^{2}$