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  1. Tomek Bartoszynski & Jaime I. Ihoda (1989). On the Cofinality of the Smallest Covering of the Real Line by Meager Sets. 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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  2. Tomek Bartoszynski, Jaime I. Ihoda & Saharon Shelah (1989). The Cofinality of Cardinal Invariants Related to Measure and Category. 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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  3. Jaime I. Ihoda & Saharon Shelah (1989). Martin's Axioms, Measurability and Equiconsistency Results. 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. Jaime I. Ihoda & Saharon Shelah (1989). Δ12-Sets of Reals. Annals of Pure and Applied Logic 42 (3):207-223.
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  5. Jaime I. Ihoda & Saharon Shelah (1989). Δ< Sup> 1< Sub> 2-Sets of Reals. Annals of Pure and Applied Logic 42 (3):207-223.
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  6. Jaime I. Ihoda (1988). Strong Measure Zero Sets and Rapid Filters. 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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  7. Jaime I. Ihoda (1988). Σ12-Sets of Reals. 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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  8. Jaime I. Ihoda (1988). $Sigma^1_2$-Sets of Reals. 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. Jaime I. Ihoda & Saharon Shelah (1988). Souslin Forcing. 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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