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  1. Perfect-set forcing for uncountable cardinals.Akihiro Kanamori - 1980 - Annals of Mathematical Logic 19 (1-2):97-114.
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  • Remarks on superatomic boolean algebras.James E. Baumgartner & Saharon Shelah - 1987 - Annals of Pure and Applied Logic 33 (C):109-129.
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  • On universal graphs without instances of CH.Saharon Shelah - 1984 - Annals of Pure and Applied Logic 26 (1):75-87.
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  • Higher Miller forcing may collapse cardinals.Heike Mildenberger & Saharon Shelah - 2021 - Journal of Symbolic Logic 86 (4):1721-1744.
    We show that it is independent whether club $\kappa $ -Miller forcing preserves $\kappa ^{++}$. We show that under $\kappa ^{ \kappa $, club $\kappa $ -Miller forcing collapses $\kappa ^{<\kappa }$ to $\kappa $. Answering a question by Brendle, Brooke-Taylor, Friedman and Montoya, we show that the iteration of ultrafilter $\kappa $ -Miller forcing does not have the Laver property.
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  • Changing cofinalities and collapsing cardinals in models of set theory.Miloš S. Kurilić - 2003 - Annals of Pure and Applied Logic 120 (1-3):225-236.
    If a˜cardinal κ1, regular in the ground model M, is collapsed in the extension N to a˜cardinal κ0 and its new cofinality, ρ, is less than κ0, then, under some additional assumptions, each cardinal λ>κ1 less than cc/[κ1]<κ1) is collapsed to κ0 as well. If in addition N=M[f], where f : ρ→κ1 is an unbounded mapping, then N is a˜λ=κ0-minimal extension. This and similar results are applied to generalized forcing notions of Bukovský and Namba.
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  • Separating families and order dimension of Turing degrees.Ashutosh Kumar & Dilip Raghavan - 2021 - Annals of Pure and Applied Logic 172 (5):102911.
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  • Power Set Modulo Small, the Singular of Uncountable Cofinality.Saharon Shelah - 2007 - Journal of Symbolic Logic 72 (1):226 - 242.
    Let μ be singular of uncountable cofinality. If μ > 2cf(μ), we prove that in P = ([μ]μ, ⊇) as a forcing notion we have a natural complete embedding of Levy (‮א‬₀, μ⁺) (so P collapses μ⁺ to ‮א‬₀) and even Levy ($(\aleph _{0},U_{J_{\kappa}^{{\rm bd}}}(\mu))$). The "natural" means that the forcing ({p ∈ [μ]μ: p closed}, ⊇) is naturally embedded and is equivalent to the Levy algebra. Also if P fails the χ-c.c. then it collapses χ to ‮א‬₀ (and the (...)
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  • Towers and clubs.Pierre Matet - 2021 - Archive for Mathematical Logic 60 (6):683-719.
    We revisit several results concerning club principles and nonsaturation of the nonstationary ideal, attempting to improve them in various ways. So we typically deal with a ideal J extending the nonstationary ideal on a regular uncountable cardinal \, our goal being to witness the nonsaturation of J by the existence of towers ).
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  • Complete Bipartite Partition Relations in Cohen Extensions.Dávid Uhrik - forthcoming - Journal of Symbolic Logic:1-8.
    We investigate the effect of adding $\omega _2$ Cohen reals on graphs on $\omega _2$, in particular we show that $\omega _2 \to (\omega _2, \omega : \omega )^2$ holds after forcing with $\mathsf {Add}(\omega, \omega _2)$ in a model of $\mathsf {CH}$. We also prove that this result is in a certain sense optimal as $\mathsf {Add}(\omega, \omega _2)$ forces that $\omega _2 \not \to (\omega _2, \omega : \omega _1)^2$.
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  • Linear orderings and powers of characterizable cardinals.Ioannis Souldatos - 2012 - Annals of Pure and Applied Logic 163 (3):225-237.
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  • Divide and Conquer: Dividing Lines and Universality.Saharon Shelah - 2021 - Theoria 87 (2):259-348.
    We discuss dividing lines (in model theory) and some test questions, mainly the universality spectrum. So there is much on conjectures, problems and old results, mainly of the author and also on some recent results.
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  • Chains in Boolean algebras.R. Mckenzie - 1982 - Annals of Mathematical Logic 22 (2):137.
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  • Non‐saturation of the non‐stationary ideal on Pκ (λ) with λ of countable cofinality.Pierre Matet - 2012 - Mathematical Logic Quarterly 58 (1-2):38-45.
    Given a regular uncountable cardinal κ and a cardinal λ > κ of cofinality ω, we show that the restriction of the non-stationary ideal on Pκ to the set of all a with equation image is not λ++-saturated . We actually prove the stronger result that there is equation image with |Q| = λ++ such that A∩B is a non-cofinal subset of Pκ for any two distinct members A, B of Q, where NGκ, λ denotes the game ideal on Pκ. (...)
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  • Independence of Boolean algebras and forcing.Miloš S. Kurilić - 2003 - Annals of Pure and Applied Logic 124 (1-3):179-191.
    If κω is a cardinal, a complete Boolean algebra is called κ-dependent if for each sequence bβ: β<κ of elements of there exists a partition of the unity, P, such that each pP extends bβ or bβ′, for κ-many βκ. The connection of this property with cardinal functions, distributivity laws, forcing and collapsing of cardinals is considered.
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  • On constructions with 2-cardinals.Piotr Koszmider - 2017 - Archive for Mathematical Logic 56 (7-8):849-876.
    We propose developing the theory of consequences of morasses relevant in mathematical applications in the language alternative to the usual one, replacing commonly used structures by families of sets originating with Velleman’s neat simplified morasses called 2-cardinals. The theory of related trees, gaps, colorings of pairs and forcing notions is reformulated and sketched from a unifying point of view with the focus on the applicability to constructions of mathematical structures like Boolean algebras, Banach spaces or compact spaces. The paper is (...)
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  • Fallen cardinals.Menachem Kojman & Saharon Shelah - 2001 - Annals of Pure and Applied Logic 109 (1-2):117-129.
    We prove that for every singular cardinal μ of cofinality ω, the complete Boolean algebra contains a complete subalgebra which is isomorphic to the collapse algebra CompCol. Consequently, adding a generic filter to the quotient algebra collapses μ0 to 1. Another corollary is that the Baire number of the space U of all uniform ultrafilters over μ is equal to ω2. The corollaries affirm two conjectures of Balcar and Simon. The proof uses pcf theory.
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  • Ideal topologies in higher descriptive set theory.Peter Holy, Marlene Koelbing, Philipp Schlicht & Wolfgang Wohofsky - 2022 - Annals of Pure and Applied Logic 173 (4):103061.
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  • Fresh function spectra.Vera Fischer, Marlene Koelbing & Wolfgang Wohofsky - 2023 - Annals of Pure and Applied Logic 174 (9):103300.
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  • Remarks on superatomic Boolean algebras.J. E. Baumgartner - 1987 - Annals of Pure and Applied Logic 33 (2):109.
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