6 found
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  1.  11
    Narrow Boolean Algebras.Robert Bonnet & Saharon Shelah - 1985 - Annals of Pure and Applied Logic 28 (1):1-12.
  2.  11
    On Well-Generated Boolean Algebras.Robert Bonnet & Matatyahu Rubin - 2000 - Annals of Pure and Applied Logic 105 (1-3):1-50.
    A Boolean algebra B that has a well-founded sublattice L which generates B is called a well-generated Boolean algebra. If in addition, L is generated by a complete set of representatives for B , then B is said to be canonically well-generated .Every WG Boolean algebra is superatomic. We construct two basic examples of superatomic non well-generated Boolean algebras. Their cardinal sequences are 1,0,1,1 and 0,0,20,1.Assuming MA , we show that every algebra with one of the cardinal sequences , α<1, (...)
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  3.  68
    Elementary Embedding Between Countable Boolean Algebras.Robert Bonnet & Matatyahu Rubin - 1991 - Journal of Symbolic Logic 56 (4):1212-1229.
    For a complete theory of Boolean algebras T, let MT denote the class of countable models of T. For B1, B2 ∈ MT, let B1 ≤ B2 mean that B1 is elementarily embeddable in B2. Theorem 1. For every complete theory of Boolean algebras T, if T ≠ Tω, then $\langle M_T, \leq\rangle$ is well-quasi-ordered. ■ We define Tω. For a Boolean algebra B, let I(B) be the ideal of all elements of the form a + s such that $B\upharpoonright (...)
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  4.  19
    On Poset Boolean Algebras of Scattered Posets with Finite Width.Robert Bonnet & Matatyahu Rubin - 2004 - Archive for Mathematical Logic 43 (4):467-476.
    We prove that the poset algebra of every scattered poset with finite width is embeddable in the poset algebra of a well ordered poset.
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  5.  24
    On Essentially Low, Canonically Well-Generated Boolean Algebras.Robert Bonnet & Matatyahu Rubin - 2002 - Journal of Symbolic Logic 67 (1):369-396.
    Let B be a superatomic Boolean algebra (BA). The rank of B (rk(B)), is defined to be the Cantor Bendixon rank of the Stone space of B. If a ∈ B - {0}, then the rank of a in B (rk(a)), is defined to be the rank of the Boolean algebra $B b \upharpoonright a \overset{\mathrm{def}}{=} \{b \in B: b \leq a\}$ . The rank of 0 B is defined to be -1. An element a ∈ B - {0} is (...)
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  6.  5
    In Memoriam: Mati Rubin 1946–2017.Assaf Hasson & Robert Bonnet - 2018 - Bulletin of Symbolic Logic 24 (2):181-185.
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