25 found
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  1.  49
    Mathematical Logic.J. Donald Monk - 1976 - Springer Verlag.
    " There are 31 chapters in 5 parts and approximately 320 exercises marked by difficulty and whether or not they are necessary for further work in the book.
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  2.  29
    Cylindric Algebras. Part I.Leon Henkin, J. Donald Monk, Alfred Tarski, L. Henkin, J. D. Monk & A. Tarski - 1985 - Journal of Symbolic Logic 50 (1):234-237.
  3.  33
    Cylindric Algebras. Part II.Leon Henkin, J. Donald Monk & Alfred Tarski - 1988 - Journal of Symbolic Logic 53 (2):651-653.
  4.  63
    Nonfinitizability of Classes of Representable Cylindric Algebras.J. Donald Monk - 1969 - Journal of Symbolic Logic 34 (3):331-343.
  5.  58
    On an Algebra of Sets of Finite Sequences.J. Donald Monk - 1970 - Journal of Symbolic Logic 35 (1):19-28.
  6.  67
    On Some Small Cardinals for Boolean Algebras.Ralph Mckenzie & J. Donald Monk - 2004 - Journal of Symbolic Logic 69 (3):674-682.
    Assume that all algebras are atomless. (1) $Spind(A x B) = Spind(A) \cup Spind(B)$ . (2) $(\prod_{i\inI}^{w} = {\omega} \cup \bigcup_{i\inI}$ $Spind(A_{i})$ . Now suppose that $\kappa$ and $\lambda$ are infinite cardinals, with $kappa$ uncountable and regular and with $\kappa \textless \lambda$ . (3) There is an atomless Boolean algebra A such that $\mathfrak{u}(A) = \kappa$ and $i(A) = \lambda$ . (4) If $\lambda$ is also regular, then there is an atomless Boolean algebra A such that $t(A) = \mathfrak{s}(A) = (...)
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  7.  73
    The Spectrum of Partitions of a Boolean Algebra.J. Donald Monk - 2001 - Archive for Mathematical Logic 40 (4):243-254.
    The main notion dealt with in this article is where A is a Boolean algebra. A partition of 1 is a family ofnonzero pairwise disjoint elements with sum 1. One of the main reasons for interest in this notion is from investigations about maximal almost disjoint families of subsets of sets X, especially X=ω. We begin the paper with a few results about this set-theoretical notion.Some of the main results of the paper are:• (1) If there is a maximal family (...)
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  8.  38
    Maximal Irredundance and Maximal Ideal Independence in Boolean Algebras.J. Donald Monk - 2008 - Journal of Symbolic Logic 73 (1):261-275.
  9. The Contributions of Alfred Tarski to Algebraic Logic.J. Donald Monk - 1986 - Journal of Symbolic Logic 51 (4):899-906.
  10.  36
    Remarks on Continuum Cardinals on Boolean Algebras.J. Donald Monk - 2012 - Mathematical Logic Quarterly 58 (3):159-167.
    We give some results concerning various generalized continuum cardinals. The results answer some natural questions which have arisen in preparing a new edition of 5. To make the paper self-contained we define all of the cardinal functions that enter into the theorems here. There are many problems concerning these new functions, and we formulate some of the more important ones.
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  11.  15
    Representable cylindric algebras.Leon Henkin, J. Donald Monk & Alfred Tarski - 1986 - Annals of Pure and Applied Logic 31:23-60.
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  12.  20
    The Mathematics of Boolean Algebra.J. Donald Monk - 2008 - Stanford Encyclopedia of Philosophy.
  13.  39
    Homogeneous Boolean Algebras with Very Nonsymmetric Subalgebras.Sabine Koppelberg & J. Donald Monk - 1983 - Notre Dame Journal of Formal Logic 24 (3):353-356.
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  14.  74
    Continuum Cardinals Generalized to Boolean Algebras.J. Donald Monk - 2001 - Journal of Symbolic Logic 66 (4):1928-1958.
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  15.  36
    On General Boundedness and Dominating Cardinals.J. Donald Monk - 2004 - Notre Dame Journal of Formal Logic 45 (3):129-146.
    For cardinals we let be the smallest size of a subset B of unbounded in the sense of ; that is, such that there is no function such that has size less than for all . Similarly for , the general dominating number, which is the smallest size of a subset B of such that for every there is an such that the above set has size less than . These cardinals are generalizations of the usual ones for . When (...)
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  16.  6
    A Large List of Small Cardinal Characteristics of Boolean Algebras.J. Donald Monk - 2018 - Mathematical Logic Quarterly 64 (4-5):336-348.
    No categories
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  17.  32
    In Memoriam: Leon Albert Henkin, 1921—2006.J. Donald Monk - 2009 - Bulletin of Symbolic Logic 15 (3):326-331.
  18.  41
    Joseph R. Shoenfield. Mathematical Logic. Republication of JSL XL 234. Association for Symbolic Logic, Urbana, and A K Peters, Natick, Mass., 2001, Viii + 344 Pp. [REVIEW]J. Donald Monk - 2001 - Bulletin of Symbolic Logic 7 (3):376.
  19.  63
    Meeting of the Association for Symbolic Logic, Dallas 1973.J. Donald Monk, Jan Mycielski & Jürgen Schmidt - 1973 - Journal of Symbolic Logic 38 (3):541-549.
  20.  37
    Roger C. Lyndon. The Representation of Relation Algebras, II. Annals of Mathematics, Ser. 2 Vol. 63 , Pp. 294–307.J. Donald Monk - 1974 - Journal of Symbolic Logic 39 (2):337.
  21.  22
    Review: Joseph R. Shoenfield, Mathematical Logic. [REVIEW]J. Donald Monk - 2001 - Bulletin of Symbolic Logic 7 (3):376-376.
  22.  32
    Review: Roger C. Lyndon, The Representation of Relation Algebras, II. [REVIEW]J. Donald Monk - 1974 - Journal of Symbolic Logic 39 (2):337-337.
  23.  28
    Special Subalgebras of Boolean Algebras.J. Donald Monk - 2010 - Mathematical Logic Quarterly 56 (2):148-158.
    We consider eight special kinds of subalgebras of Boolean algebras. In Section 1 we describe the relationships between these subalgebra notions. In succeeding sections we consider how the subalgebra notions behave with respect to the most common cardinal functions on Boolean algebras.
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  24.  37
    The Spectrum of Maximal Independent Subsets of a Boolean Algebra.J. Donald Monk - 2004 - Annals of Pure and Applied Logic 126 (1-3):335-348.
    Recall that a subset X of a Boolean algebra A is independent if for any two finite disjoint subsets F , G of X we have ∏ x∈F x ∏ y∈G −y≠0. The independence of a BA A , denoted by Ind, is the supremum of cardinalities of its independent subsets. We can also consider the maximal independent subsets. The smallest size of an infinite maximal independent subset is the cardinal invariant i , well known in the case A= P (...)
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  25. REVIEWS-Mathematical Logic.J. Shoenfield & J. Donald Monk - 2001 - Bulletin of Symbolic Logic 7 (3):376-376.