22 found
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  1.  14
    Maximally Embeddable Components.Miloš S. Kurilić - 2013 - Archive for Mathematical Logic 52 (7-8):793-808.
    We investigate the partial orderings of the form ${\langle \mathbb{P}(\mathbb{X}), \subset \rangle}$ , where ${\mathbb{X} =\langle X, \rho \rangle }$ is a countable binary relational structure and ${\mathbb{P} (\mathbb{X})}$ the set of the domains of its isomorphic substructures and show that if the components of ${\mathbb{X}}$ are maximally embeddable and satisfy an additional condition related to connectivity, then the poset ${\langle \mathbb{P} (\mathbb{X}), \subset \rangle }$ is forcing equivalent to a finite power of (P(ω)/ Fin)+, or to the poset (P(ω (...)
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  2.  12
    Condensational Equivalence, Equimorphism, Elementary Equivalence and Similar Similarities.Miloš S. Kurilić & Nenad Morača - 2017 - Annals of Pure and Applied Logic 168 (6):1210-1223.
  3.  10
    From A1 to D5: Towards a Forcing-Related Classification of Relational Structures.Miloš S. Kurilić - 2014 - Journal of Symbolic Logic 79 (1):279-295.
  4.  9
    Posets of Copies of Countable Scattered Linear Orders.Miloš S. Kurilić - 2014 - Annals of Pure and Applied Logic 165 (3):895-912.
    We show that the separative quotient of the poset 〈P,⊂〉 of isomorphic suborders of a countable scattered linear order L is σ-closed and atomless. So, under the CH, all these posets are forcing-equivalent /Fin)+).
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  5.  13
    Forcing by Non-Scattered Sets.Miloš S. Kurilić & Stevo Todorčević - 2012 - Annals of Pure and Applied Logic 163 (9):1299-1308.
  6.  9
    Isomorphic and Strongly Connected Components.Miloš S. Kurilić - 2015 - Archive for Mathematical Logic 54 (1-2):35-48.
    We study the partial orderings of the form ⟨P,⊂⟩\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\langle \mathbb{P}, \subset\rangle}$$\end{document}, where X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{X}}$$\end{document} is a binary relational structure with the connectivity components isomorphic to a strongly connected structure Y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{Y}}$$\end{document} and P\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{P} }$$\end{document} is the set of substructures of X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} (...)
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  7.  4
    Different Similarities.Miloš S. Kurilić - 2015 - Archive for Mathematical Logic 54 (7-8):839-859.
    We establish the hierarchy among twelve equivalence relations on the class of relational structures: the equality, the isomorphism, the equimorphism, the full relation, four similarities of structures induced by similarities of their self-embedding monoids and intersections of these equivalence relations. In particular, fixing a language L and a cardinal κ, we consider the interplay between the restrictions of these similarities to the class ModL of all L-structures of size κ. It turns out that, concerning the number of different similarities and (...)
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  8.  18
    Cohen-Stable Families of Subsets of Integers.Miloš S. Kurilić - 2001 - Journal of Symbolic Logic 66 (1):257-270.
    A maximal almost disjoint (mad) family $\mathscr{A} \subseteq [\omega]^\omega$ is Cohen-stable if and only if it remains maximal in any Cohen generic extension. Otherwise it is Cohen-unstable. It is shown that a mad family, A, is Cohen-unstable if and only if there is a bijection G from ω to the rationals such that the sets G[A], A ∈A are nowhere dense. An ℵ 0 -mad family, A, is a mad family with the property that given any countable family $\mathscr{B} \subset (...)
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  9.  9
    The Poset of All Copies of the Random Graph has the 2-Localization Property.Miloš S. Kurilić & Stevo Todorčević - 2016 - Annals of Pure and Applied Logic 167 (8):649-662.
  10.  12
    A Posteriori Convergence in Complete Boolean Algebras with the Sequential Topology.Miloš S. Kurilić & Aleksandar Pavlović - 2007 - Annals of Pure and Applied Logic 148 (1):49-62.
    A sequence x=xn:nω of elements of a complete Boolean algebra converges to a priori if lim infx=lim supx=b. The sequential topology τs on is the maximal topology on such that x→b implies x→τsb, where →τs denotes the convergence in the space — the a posteriori convergence. These two forms of convergence, as well as the properties of the sequential topology related to forcing, are investigated. So, the a posteriori convergence is described in terms of killing of tall ideals on ω, (...)
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  11.  2
    Reversibility of Extreme Relational Structures.Miloš S. Kurilić & Nenad Morača - forthcoming - Archive for Mathematical Logic:1-18.
    A relational structure \ is called reversible iff each bijective homomorphism from \ onto \ is an isomorphism, and linear orders are prototypical examples of such structures. One way to detect new reversible structures of a given relational language L is to notice that the maximal or minimal elements of isomorphism-invariant sets of interpretations of the language L on a fixed domain X determine reversible structures. We isolate certain syntactical conditions providing that a satisfiable \-theory defines a class of interpretations (...)
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  12.  2
    Reversibility of Extreme Relational Structures.Miloš S. Kurilić & Nenad Morača - forthcoming - Archive for Mathematical Logic:1-18.
    A relational structure \ is called reversible iff each bijective homomorphism from \ onto \ is an isomorphism, and linear orders are prototypical examples of such structures. One way to detect new reversible structures of a given relational language L is to notice that the maximal or minimal elements of isomorphism-invariant sets of interpretations of the language L on a fixed domain X determine reversible structures. We isolate certain syntactical conditions providing that a satisfiable \-theory defines a class of interpretations (...)
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  13.  8
    Vaught's Conjecture for Monomorphic Theories.Miloš S. Kurilić - 2019 - Annals of Pure and Applied Logic 170 (8):910-920.
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  14.  16
    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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  15.  7
    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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  16.  1
    Reversibility of Extreme Relational Structures.Miloš S. Kurilić & Nenad Morača - forthcoming - Archive for Mathematical Logic:1-18.
    A relational structure \ is called reversible iff each bijective homomorphism from \ onto \ is an isomorphism, and linear orders are prototypical examples of such structures. One way to detect new reversible structures of a given relational language L is to notice that the maximal or minimal elements of isomorphism-invariant sets of interpretations of the language L on a fixed domain X determine reversible structures. We isolate certain syntactical conditions providing that a satisfiable \-theory defines a class of interpretations (...)
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  17.  16
    Power-Collapsing Games.Miloš S. Kurilić & Boris Šobot - 2008 - Journal of Symbolic Logic 73 (4):1433-1457.
    The game Gls(κ) is played on a complete Boolean algebra B, by two players. White and Black, in κ-many moves (where κ is an infinite cardinal). At the beginning White chooses a non-zero element p ∈ B. In the α-th move White chooses pα ∈ (0.p)p and Black responds choosing iα ∈ {0.1}. White wins the play iff $\bigwedge _{\beta \in \kappa}\bigvee _{\alpha \geq \beta }p_{\alpha}^{i\alpha}=0$ , where $p_{\alpha}^{0}=p_{\alpha}$ and $p_{\alpha}^{1}=p\ p_{\alpha}$ . The corresponding game theoretic properties of c.B.a.'s are (...)
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  18.  8
    Mad Families, Forcing and the Suslin Hypothesis.Miloš S. Kurilić - 2004 - Archive for Mathematical Logic 44 (4):499-512.
    Let κ be a regular cardinal and P a partial ordering preserving the regularity of κ. If P is (κ-Baire and) of density κ, then there is a mad family on κ killed in all generic extensions (if and) only if below each p∈P there exists a κ-sized antichain. In this case a mad family on κ is killed (if and) only if there exists an injection from κ onto a dense subset of Ult(P) mapping the elements of onto nowhere (...)
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  19.  5
    Unsupported Boolean Algebras and Forcing.Miloš S. Kurilić - 2004 - Mathematical Logic Quarterly 50 (6):594-602.
    If κ is an infinite cardinal, a complete Boolean algebra B is called κ-supported if for each sequence 〈bβ : β αbβ = equation imagemath imageequation imageβ∈Abβ holds. Combinatorial and forcing equivalents of this property are given and compared with the other forcing related properties of Boolean algebras . The set of regular cardinals κ for which B is not κ-supported is investigated.
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  20.  14
    A Game on Boolean Algebras Describing the Collapse of the Continuum.Miloš S. Kurilić & Boris Šobot - 2009 - Annals of Pure and Applied Logic 160 (1):117-126.
    The game is played on a complete Boolean algebra in ω-many moves. At the beginning White chooses a non-zero element p of and, in the nth move, White chooses a positive pn

    (...)

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  21.  12
    Splitting Families and Forcing.Miloš S. Kurilić - 2007 - Annals of Pure and Applied Logic 145 (3):240-251.
    According to [M.S. Kurilić, Cohen-stable families of subsets of the integers, J. Symbolic Logic 66 257–270], adding a Cohen real destroys a splitting family on ω if and only if is isomorphic to a splitting family on the set of rationals, , whose elements have nowhere dense boundaries. Consequently, implies the Cohen-indestructibility of . Using the methods developed in [J. Brendle, S. Yatabe, Forcing indestructibility of MAD families, Ann. Pure Appl. Logic 132 271–312] the stability of splitting families in several (...)
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  22.  7
    Property {(Hbar)} and Cellularity of Complete Boolean Algebras.Miloš S. Kurilić & Stevo Todorčević - 2009 - Archive for Mathematical Logic 48 (8):705-718.
    A complete Boolean algebra ${\mathbb{B}}$ satisfies property ${(\hbar)}$ iff each sequence x in ${\mathbb{B}}$ has a subsequence y such that the equality lim sup z n = lim sup y n holds for each subsequence z of y. This property, providing an explicit definition of the a posteriori convergence in complete Boolean algebras with the sequential topology and a characterization of sequential compactness of such spaces, is closely related to the cellularity of Boolean algebras. Here we determine the position of (...)
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