9 citations · 34 across the 60 of their papers we have counts for
75 papers
Strong Completeness of Provability Logic for Uncountable Languages
Mohammad Golshani, Grigorii Stepanov, Reihane Zoghifard
For an ordinal , we use the Erdős--Rado partition theorem to prove the failure of strong completeness of for modal languages of cardinality $(2^{|λ|+\aleph_0})^{…
Quite free p-groups with trivial duality
Mohsen Asgharzadeh, Mohammad Golshani, Saharon Shelah
We present a class of abelian groups that exhibit a high degree of freeness while possessing no non-trivial homomorphisms to a canonical free object. Unlike prior investigations, w…
On groups well represented as automorphism groups of groups
Mohsen Asgharzadeh, Mohammad Golshani, Daniel Herden +1
Assuming Gödel's axiom of constructibility we present a characterization of those groups for which there exist arbitrarily large groups such that $aut(H)…
Adding highly undefinable sets over
Mohammad Golshani, Saharon Shelah
We sow that there exists a generic extension of the Gödel's constructible universe in which diamond holds and there exists a subset such that for stationary many…
Cohen Generic Structures with Functions
Nathanael Ackerman, Mohammad Golshani, Mostafa Mirabi
Suppose are languages where is relational. Additionally, let be a strong c…
Expressive Power of Infinitary Logic and Absolute co-Hopfianity
Mohsen Asgharzadeh, Mohammad Golshani, Saharon Shelah
Recently, Paolini and Shelah have constructed absolutely Hopfian torsion-free abelian groups of any given size. In contrast, we show that this is not necessarily the case for absol…
Naturality and Definability III
Mohsen Asgharzadeh, Mohammad Golshani, Saharon Shelah
In this paper, we deal with the notions of naturality from category theory and definablity from model theory and their interactions. In this regard, we present three results. First…
A generic absoluteness principle consistent with large continuum
Mohammad Golshani
We state a new generic absoluteness principle, and use Shelah's memory iteration technique to show that it is consistent with the large continuum.
The Abraham-Shelah -well-ordering of the reals
Mohammad Golshani
We give an exposition of the Abraham-Shelah's proof of the consistency of with existence of a -well-ordering of the reals.
Adding highly generic subsets of
Esfandiar Eslami, Mohammad Golshani, Rouholah Hoseini Naveh
Starting from the we build a cardinal and preserving generic extension of the universe, in which there exists a set of size so t…
Co-Hopfian and boundedly endo-rigid mixed abelian groups
Mohsen Asgharzadeh, Mohammad Golshani, Saharon Shelah
For a given cardinal and a torsion abelian group of cardinality less than , we present, under some mild conditions (for example ), boundedly endo-rigid a…
The proper forcing axiom for -sized posets, -linked symmetrically proper forcing, and the size of the continuum
David Asperó, Mohammad Golshani
We show that the Proper Forcing Axiom for forcing notions of size is consistent with the continuum being arbitrarily large. In fact, assuming holds and …
The measuring principle and the continuum hypothesis
Mohammad Golshani, Saharon Shelah
We show that one can force the Measuring principle without adding any new reals. We also show that it is consistent with the large continuum. These results answer two famous questi…
No universal graphs at uncountable regular cardinals
Mohammad Golshani
Assuming the existence of a strong cardinal, we find a model of ZFC in which for each uncountable regular cardinal there is no universal graph of size .
Unlimited accumulation by the Shelah's PCF operator
Mohammad Golshani
Modulo the existence of large cardinals, there is a model of set theory in which for some set of regular cardinals, the sequence $\langle \text{pcf}^α(B): α\in \text{Ord} \rang…
Representing the language of a topos as quotient of the category of spans
M. Golshani, A. Shiralinasab Langari
We use quotients of span categories to introduce the language of a topos. We also study the logical relations and the quotients of span categories derived from them. As an applicat…
The Keisler-Shelah isomorphism theorem and the continuum hypothesis II
Mohammad Golshani, Saharon Shelah
We continue the investigation started in [Sh:1215] about the relation between the Keilser-Shelah isomorphism theorem and the continuum hypothesis. In particular, we show it is cons…
Graphs represented by Ext
Mohsen Asgharzadeh, Mohammad Golshani, Saharon Shelah
This paper opens and discusses the question originally due to Daniel Herden, who asked for which graph we can find a family of abelian groups such t…
Completeness of the Gödel-Löb provability logic for the filter sequence of normal measures
Mohammad Golshani, Reihane Zoghifard
Assuming the existence of suitable large cardinals, we show it is consistent that the Provability logic is complete with respect to the filter sequence of normal meas…
The Keisler-Shelah isomorphism theorem and the continuum hypothesis
Mohammad Golshani, Saharon Shelah
We show that if for any two elementary equivalent structures of size at most continuum in a countable language, $\mathbf{M}^ω/ \mathcal{U} \simeq \mathbf{N…
Kaplansky Test Problems for -Modules in ZFC
Mohsen Asgharzadeh, Mohammad Golshani, Saharon Shelah
Fix a ring and look at the class of left -modules and naturally, we restrict ourselves to the case of rings such that this class is not too similar to the case is…
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…
Combinatorial and number-theoretic properties of generic reals
Will Brian, Mohammad Golshani
We discuss some properties of Cohen and random reals. We show that they belong to any definable partition regular family, and hence they satisfy most "largeness" properties studied…
Two remarks on Merimovich's model of the total failure of GCH
Mohammad Golshani
Let denote the Merimovich's model in which for each infinite cardinal . We show that in the following hold: (1) Shelah's strong hypothesis fails at all singu…