9 citations · 34 across the 60 of their papers we have counts for
15 papers · 1 filter
The tree property at double successors of singular cardinals of uncountable cofinality
Mohammad Golshani, Rahman Mohammadpour
Assuming the existence of a strong cardinal and a measurable cardinal above it, we force a generic extension in which is a singular strong limit cardinal of any prescribed…
Notes on countably generated complete Boolean algebras
Mohammad Golshani
We give a necessary and sufficient condition for an atomless Boolean algebra to be countably generated, and use it to give new proofs of some some know facts due to Gaifman-Hales a…
On the classification of definable ccc forcing notions
Mohammad Golshani, Haim Horowitz, Saharon Shelah
We show that for a Suslin ccc forcing notion adding a Hechler real, ``all sets of reals are -measurable'' implies th…
The Special Aronszajn Tree Property
Mohammad Golshani, Yair Hayut
Assuming the existence of a proper class of supercompact cardinals, we force that for every regular cardinal , there are -Aronszajn trees and all such trees are special.
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 giv…
All uncountable regular cardinals can be inaccessible in HOD
Mohammad Golshani
Assuming the existence of a supercompact cardinal and an inaccessible above it, we construct a model of ZFC, in which all uncountable regular cardinals are inaccessible in HOD.
Definable tree property for uncountable regular cardinals
Mohammad Golshani, Mostafa Mirabi
The primary goal of this paper is to establish a model of wherein the definable tree property is affirmed for all uncountable regular cardinals. This endeavor commences with…
(Weak) diamond can fail at the least inaccessible cardinal
Mohammad Golshani
Starting from suitable large cardinals, we force the failure of (weak) diamond at the least inaccessible cardinal. The result improves an unpublished theorem of Woodin and a recent…
On cuts in ultraproducts of linear orders II
Mohammad Golshani, Saharon Shelah
We continue our study of the class , where is a uniform ultrafilter on a cardinal and is the class of all pairs where $(θ_1,…
An Easton like theorem in the presence of Shelah Cardinals
Mohammad Golshani
We show that Shelah cardinals are preserved under the canonical forcing notion. We also show that if holds and is an Easton function which satis…
On a question of Zadrozny
Mohammad Golshani
We answer a question of Zadrozny.
Power set at : On a theorem of Woodin
Mohammad Golshani
We give Woodin's original proof that if there exists a strong cardinal then there is a generic extension of the universe in which holds below $\ale…
Collapsing the cardinals of
James Cummings, Sy David Friedman, Mohammad Golshani
Assuming that holds and is -supercompact, we construct a generic extension of in which remains strongly inaccessible and for every…
A Groszek-Laver pair of undistinguishable classes
Mohammad Golshani, Vladimir Kanovei, Vassily A Lyubetsky
A generic extension of by reals is defined, in which the union of -classes of and is a set, but neither of these two -c…
Tree property at successor of a singular limit of measurable cardinals
Mohammad Golshani
Assume is a singular limit of supercompact cardinals, where is a limit ordinal. We present two forcing methods for making the successor of the limit of the…