11 found
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  1.  20
    Superatomic Boolean Algebras Constructed From Morasses.Peter Koepke & Juan Carlos Martínez - 1995 - Journal of Symbolic Logic 60 (3):940-951.
    By using the notion of a simplified (κ,1)-morass, we construct κ-thin-tall, κ-thin-thick and, in a forcing extension, κ-very thin-thick superatomic Boolean algebras for every infinite regular cardinal κ.
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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. Accessible Sets and (Lω1ω)T-Equivalence for T3 Spaces.Juan Carlos Martínez - 1984 - Journal of Symbolic Logic 49 (3):961 - 967.
  4. On Topological Spaces Equivalent to Ordinals.Jörg Flum & Juan Carlos Martinez - 1988 - Journal of Symbolic Logic 53 (3):785-795.
    Let L be one of the topological languages L t , (L ∞ω ) t and (L κω ) t . We characterize the topological spaces which are models of the L-theory of the class of ordinals equipped with the order topology. The results show that the role played in classical model theory by the property of being well-ordered is taken over in the topological context by the property of being locally compact and scattered.
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  5.  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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  6.  10
    Some Open Questions for Superatomic Boolean Algebras.Juan Carlos Martínez - 2005 - Notre Dame Journal of Formal Logic 46 (3):353-356.
    In connection with some known results on uncountable cardinal sequences for superatomic Boolean algebras, we shall describe some open questions for superatomic Boolean algebras concerning singular cardinals.
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  7.  32
    Productos de Lt-tipos para especies T.Juan Carlos Martinez - 1992 - Theoria 7 (1/2/3):105-121.
    It is a wel known fact that the finite products of Hintikka-Fraissé types for sentences of quantifier rank n give rise to the set of atoms of a finite boolean algebra. In this paper we consider the class of (Lww)t-types introduced in [4], which caracterizes in a pure topological way the (Lww)t-equivalence for T3 spaces. We define for every nonempty family I of n-types a product xInai in such a way that if I is a family of T3 spaces, XIAi (...)
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  8.  29
    Álgebras de Boole Y Lógica.Juan Carlos Martínez - 1990 - Theoria 5 (1):269-270.
  9.  9
    On Uncountable Cardinal Sequences for Superatomic Boolean Algebras.Juan Carlos Martínez - 1995 - Archive for Mathematical Logic 34 (4):257-261.
    The countable sequences of cardinals which arise as cardinal sequences of superatomic Boolean algebras were characterized by La Grange on the basis of ZFC set theory. However, no similar characterization is available for uncountable cardinal sequences. In this paper we prove the following two consistency results:Ifθ = 〈κ α :α <ω 1〉 is a sequence of infinite cardinals, then there is a cardinal-preserving notion of forcing that changes cardinal exponentiation and forces the existence of a superatomic Boolean algebraB such that (...)
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  10.  18
    Decision Procedure for a Class of $(L{\Omega_1\Omega})_t$-Types of $T3$ Spaces.Juan Carlos Martínez - 1987 - Notre Dame Journal of Formal Logic 28 (2):284-290.
  11.  8
    Attainment of Tightness in Boolean Spaces.Juan Carlos Martínez - 2002 - Mathematical Logic Quarterly 48 (4):555-558.
    We consider some questions of Donald Monk related to attainment of the tightness function in Boolean spaces. Then we prove in ZFC that attainment of tightness in the sense of the definition does not imply attainment of tightness in the free sequence sense. Our results give rise to full answers to [2, Problems 41, 42].
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