4 found
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  1.  36
    The tree property at double successors of singular cardinals of uncountable cofinality.Mohammad Golshani & Rahman Mohammadpour - 2018 - Annals of Pure and Applied Logic 169 (2):164-175.
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  2.  22
    Guessing models and the approachability ideal.Rahman Mohammadpour & Boban Veličković - 2020 - Journal of Mathematical Logic 21 (2):2150003.
    Starting with two supercompact cardinals we produce a generic extension of the universe in which a principle that we call GM+ holds. This principle implies ISP and ISP, and hence th...
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  3.  21
    New methods in forcing iteration and applications.Rahman Mohammadpour - 2023 - Bulletin of Symbolic Logic 29 (2):300-302.
    The Theme. Strong forcing axioms like Martin’s Maximum give a reasonably satisfactory structural analysis of $H(\omega _2)$. A broad program in modern Set Theory is searching for strong forcing axioms beyond $\omega _1$. In other words, one would like to figure out the structural properties of taller initial segments of the universe. However, the classical techniques of forcing iterations seem unable to bypass the obstacles, as the resulting forcings axioms beyond $\omega _1$ have not thus far been strong enough! However, (...)
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  4.  66
    Specialising Trees with Small Approximations I.Rahman Mohammadpour - forthcoming - Journal of Symbolic Logic:1-24.
    Assuming $\mathrm{PFA}$, we shall use internally club $\omega _1$ -guessing models as side conditions to show that for every tree T of height $\omega _2$ without cofinal branches, there is a proper and $\aleph _2$ -preserving forcing notion with finite conditions which specialises T. Moreover, the forcing has the $\omega _1$ -approximation property.
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