From the 1 of 11 linked papers with an AI index.
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Strong Completeness of Provability Logic for Uncountable Languages
Mohammad Golshani, Grigorii Stepanov, Reihane Zoghifard
For an ordinal , we use the ErdÅs--Rado partition theorem to prove the failure of strong completeness of for modal languages of cardinality $(2^{|λ|+\aleph_0}…
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…
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 $κ\geqÏ_2…
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…
On a Question of Hamkins and Löwe on the modal logic of collapse forcing
Mohammad Golshani, William Mitchell
Hamkins and Löwe asked whether there can be a model of set theory with the property that whenever is a generic collapse of a cardinal of onto . We g…
Cohen Generic Structures with Functions
Nathanael Ackerman, Mohammad Golshani, Mostafa Mirabi
Suppose are languages where is relational. Additionally, let be a strong …