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  1. The Cofinality of Cardinal Invariants Related to Measure and Category.Tomek Bartoszynski, Jaime I. Ihoda & Saharon Shelah - 1989 - Journal of Symbolic Logic 54 (3):719-726.
    We prove that the following are consistent with ZFC. 1. 2 ω = ℵ ω 1 + K C = ℵ ω 1 + K B = K U = ω 2 (for measure and category simultaneously). 2. 2 ω = ℵ ω 1 = K C (L) + K C (M) = ω 2 . This concludes the discussion about the cofinality of K C.
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  2. Σ12-Sets of Reals.Jaime I. Ihoda - 1988 - Journal of Symbolic Logic 53 (2):636 - 642.
    We prove that the only implications between four notions for Σ 1 2 -sets of reals are $\Sigma^1_2-\text{measurability} \Rightarrow \Sigma^1_2-\text{categoricity} \big\downarrow \Sigma^1_2-\text{Ramsey} \Rightarrow \Sigma^1_2-K_\sigma-\text{regular}$.
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  3. Martin's Axioms, Measurability and Equiconsistency Results.Jaime I. Ihoda & Saharon Shelah - 1989 - Journal of Symbolic Logic 54 (1):78-94.
    We deal with the consistency strength of ZFC + variants of MA + suitable sets of reals are measurable (and/or Baire, and/or Ramsey). We improve the theorem of Harrington and Shelah [2] repairing the asymmetry between measure and category, obtaining also the same result for Ramsey. We then prove parallel theorems with weaker versions of Martin's axiom (MA(σ-centered), (MA(σ-linked)), MA(Γ + ℵ 0 ), MA(K)), getting Mahlo, inaccessible and weakly compact cardinals respectively. We prove that if there exists r ∈ (...)
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  4. Δ12-Sets of Reals.Jaime I. Ihoda & Saharon Shelah - 1989 - Annals of Pure and Applied Logic 42 (3):207-223.
  5.  7
    On the Cofinality of the Smallest Covering of the Real Line by Meager Sets.Tomek Bartoszynski & Jaime I. Ihoda - 1989 - Journal of Symbolic Logic 54 (3):828-832.
    We prove that the cofinality of the smallest covering of R by meager sets is bigger than the additivity of measure.
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  6.  8
    Souslin Forcing.Jaime I. Ihoda & Saharon Shelah - 1988 - Journal of Symbolic Logic 53 (4):1188-1207.
    We define the notion of Souslin forcing, and we prove that some properties are preserved under iteration. We define a weaker form of Martin's axiom, namely MA(Γ + ℵ 0 ), and using the results on Souslin forcing we show that MA(Γ + ℵ 0 ) is consistent with the existence of a Souslin tree and with the splitting number s = ℵ 1 . We prove that MA(Γ + ℵ 0 ) proves the additivity of measure. Also we introduce (...)
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  7.  7
    Strong Measure Zero Sets and Rapid Filters.Jaime I. Ihoda - 1988 - Journal of Symbolic Logic 53 (2):393-402.
    We prove that $\operatorname{cons}(ZF)$ implies $\operatorname{cons}(ZF +$ Borel conjecture + there exists a Ramsey ultrafilter). We also prove some results on strong measure zero sets from the existence of generalized Luzin sets. We study the relationships between strong measure zero sets and rapid filters on ω.
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  8.  1
    $Sigma^1_2$-Sets of Reals.Jaime I. Ihoda - 1988 - Journal of Symbolic Logic 53 (2):636-642.
    We prove that the only implications between four notions for $\Sigma^1_2$-sets of reals are $\Sigma^1_2-\text{measurability} \Rightarrow \Sigma^1_2-\text{categoricity} \big\downarrow \Sigma^1_2-\text{Ramsey} \Rightarrow \Sigma^1_2-K_\sigma-\text{regular}$.
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  9. -Sets of Reals.Jaime I. Ihoda - 1988 - Journal of Symbolic Logic 53 (2):636-642.
  10. Δ< Sup> 1< Sub> 2-Sets of Reals.Jaime I. Ihoda & Saharon Shelah - 1989 - Annals of Pure and Applied Logic 42 (3):207-223.