9 citations · 34 across the 60 of their papers we have counts for
68 papers · 1 filter
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})^{…
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…
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…
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…
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…
On slow minimal reals I
Mohammad Golshani, Saharon Shelah
Answering a question of Harrington, we show that there exists a proper forcing notion, which adds a minimal real , which is eventually different from any ol…
Strongly compct diagonal Prikry forcing
Mohammad Golshani
We define a version of Gitik-Sharon diagonal Prikry forcing using a strongly compact cardinal, and prove its basic properties.
Changing measurable into small accessible cardinals
Mohammad Golshani
We give a detailed proof of the properties of the usual Prikry type forcing notion for turning a measurable cardinal into .
Fraïssé limit via forcing
Mohammad Golshani
Given a Fraïssé class and an infinite cardinal we define a forcing notion which adds a structure of size using elements of , which extends the F…
The special Aronszajn tree property at and
David Asperó, Mohammad Golshani
Starting from the existence of a weakly compact cardinal, we build a generic extension of the universe in which holds and all -Aronszajn trees are special and hence…
The tree property at double successors of singular cardinals of uncountable cofinality with infinite gaps
Mohammad Golshani, Alejandro Poveda
Assuming the existence of a strong cardinal , a weakly compact cardinal above it and we force a generic extension in which is a singular strong limit cardinal of…