Displaying similar documents to “Properties of forcing preserved by finite support iterations”

A note on noninterpretability in o-minimal structures

Ricardo Bianconi (1998)

Fundamenta Mathematicae

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We prove that if M is an o-minimal structure whose underlying order is dense then Th(M) does not interpret the theory of an infinite discretely ordered structure. We also make a conjecture concerning the class of the theory of an infinite discretely ordered o-minimal structure.

Monotone σ-complete groups with unbounded refinement

Friedrich Wehrung (1996)

Fundamenta Mathematicae

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The real line ℝ may be characterized as the unique non-atomic directed partially ordered abelian group which is monotone σ-complete (countable increasing bounded sequences have suprema), has the countable refinement property (countable sums ∑ m a m = ∑ n b n of positive (possibly infinite) elements have common refinements) and is linearly ordered. We prove here that the latter condition is not redundant, thus solving an old problem by A. Tarski, by proving that there are many spaces (in particular,...

Goldstern–Judah–Shelah preservation theorem for countable support iterations

Miroslav Repický (1994)

Fundamenta Mathematicae

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[1] T. Bartoszyński, Additivity of measure implies additivity of category, Trans. Amer. Math. Soc. 281 (1984), 209-213. [2] T. Bartoszyński and H. Judah, Measure and Category, in preparation. [3] D. H. Fremlin, Cichoń’s diagram, Publ. Math. Univ. Pierre Marie Curie 66, Sém. Initiation Anal., 1983/84, Exp. 5, 13 pp. [4] M. Goldstern, Tools for your forcing construction, in: Set Theory of the Reals, Conference of Bar-Ilan University, H. Judah (ed.), Israel Math. Conf. Proc. 6, 1992, 307-362....

A characterization of some additive arithmetical functions, III

Jean-Loup Mauclaire (1999)

Acta Arithmetica

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I. Introduction. In 1946, P. Erdős [2] proved that if a real-valued additive arithmetical function f satisfies the condition: f(n+1) - f(n) → 0, n → ∞, then there exists a constant C such that f(n) = C log n for all n in ℕ*. Later, I. Kátai [3,4] was led to conjecture that it was possible to determine additive arithmetical functions f and g satisfying the condition: there exist a real number l, a, c in ℕ*, and integers b, d such that f(an+b) - g(cn+d) → l, n → ∞. This problem...

Diagonal conditions in ordered spaces

Harold Bennett, David Lutzer (1997)

Fundamenta Mathematicae

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For a space X and a regular uncountable cardinal κ ≤ |X| we say that κ ∈ D(X) if for each T ⊂ X 2 - Δ ( X ) with |T| = κ, there is an open neighborhood W of Δ(X) such that |T - W| = κ. If ω 1 ∈ D ( X ) then we say that X has a small diagonal, and if every regular uncountable κ ≤ |X| belongs to D(X) then we say that X has an H-diagonal. In this paper we investigate the interplay between D(X) and topological properties of X in the category of generalized ordered spaces. We obtain cardinal invariant theorems and metrization...

Products of completion regular measures

David Fremlin, S. Grekas (1995)

Fundamenta Mathematicae

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We investigate the products of topological measure spaces, discussing conditions under which all open sets will be measurable for the simple completed product measure, and under which the product of completion regular measures will be completion regular. In passing, we describe a new class of spaces on which all completion regular Borel probability measures are τ-additive, and which have other interesting properties.

On absolutely divergent series

Sakaé Fuchino, Heike Mildenberger, Saharon Shelah, Peter Vojtáš (1999)

Fundamenta Mathematicae

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We show that in the ℵ 2 -stage countable support iteration of Mathias forcing over a model of CH the complete Boolean algebra generated by absolutely divergent series under eventual dominance is not isomorphic to the completion of P(ω)/fin. This complements Vojtáš’ result that under c f ( ) = the two algebras are isomorphic [15].

On open maps of Borel sets

A. Ostrovsky (1995)

Fundamenta Mathematicae

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We answer in the affirmative [Th. 3 or Corollary 1] the question of L. V. Keldysh [5, p. 648]: can every Borel set X lying in the space of irrational numbers ℙ not G δ · F σ and of the second category in itself be mapped onto an arbitrary analytic set Y ⊂ ℙ of the second category in itself by an open map? Note that under a space of the second category in itself Keldysh understood a Baire space. The answer to the question as stated is negative if X is Baire but Y is not Baire.