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  1.  7
    Sticks and Clubs.Sakaé Fuchino, Saharon Shelah & Lajos Soukup - 1997 - Annals of Pure and Applied Logic 90 (1):57-77.
    We study combinatorial principles known as stick and club. Several variants of these principles and cardinal invariants connected to them are also considered. We introduce a new kind of side by-side product of partial orderings which we call pseudo-product. Using such products, we give several generic extensions where some of these principles hold together with ¬CH and Martin's axiom for countable p.o.-sets. An iterative version of the pseudo-product is used under an inaccessible cardinal to show the consistency of the club (...)
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  2. Cardinal Sequences of LCS Spaces Under GCH.Juan Carlos Martinez & Lajos Soukup - 2010 - Annals of Pure and Applied Logic 161 (9):1180-1193.
    Let denote the class of all cardinal sequences of length α associated with compact scattered spaces. Also put If λ is a cardinal and α λ1>>λn−1 and ordinals α0,…,αn−1 such that α=α0++αn−1 and where each .The proofs are based on constructions of universal locally compact scattered spaces.
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  3.  10
    Superatomic Boolean Algebras Constructed From Strongly Unbounded Functions.Juan Carlos Martínez & Lajos Soukup - 2011 - Mathematical Logic Quarterly 57 (5):456-469.
    Using Koszmider's strongly unbounded functions, we show the following consistency result: Suppose that κ, λ are infinite cardinals such that κ++ + ≤ λ, κ<κ = κ and 2κ = κ+, and η is an ordinal with κ+ ≤ η < κ++ and cf = κ+. Then, in some cardinal-preserving generic extension there is a superatomic Boolean algebra equation image such that equation image, equation image for every α < η and equation image. Especially, equation image and equation image can (...)
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  4.  8
    Infinite Combinatorics Plain and Simple.Dániel T. Soukup & Lajos Soukup - 2018 - Journal of Symbolic Logic 83 (3):1247-1281.
    We explore a general method based on trees of elementary submodels in order to present highly simplified proofs to numerous results in infinite combinatorics. While countable elementary submodels have been employed in such settings already, we significantly broaden this framework by developing the corresponding technique for countably closed models of size continuum. The applications range from various theorems on paradoxical decompositions of the plane, to coloring sparse set systems, results on graph chromatic number and constructions from point-set topology. Our main (...)
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  5.  17
    On the Weak Freese-Nation Property of Complete Boolean Algebras.Sakaé Fuchino, Stefan Geschke, Saharon Shelah & Lajos Soukup - 2001 - Annals of Pure and Applied Logic 110 (1-3):89-105.
    The following results are proved: In a model obtained by adding ℵ 2 Cohen reals , there is always a c.c.c. complete Boolean algebra without the weak Freese-Nation property. Modulo the consistency strength of a supercompact cardinal , the existence of a c.c.c. complete Boolean algebra without the weak Freese-Nation property is consistent with GCH. If a weak form of □ μ and cof =μ + hold for each μ >cf= ω , then the weak Freese-Nation property of 〈 P (...)
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