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Creators/Authors contains: "Poveda, Alejandro"

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  1. ; ; (, Bulletin of the London Mathematical Society)
    Abstract We strengthen a result of Bagaria and Magidor (Trans. Amer. Math. Soc.366(2014), no. 4, 1857–1877)  about the relationship between large cardinals and torsion classes of abelian groups, and prove thattheMaximum Deconstructibilityprinciple introduced in Cox (J. Pure Appl. Algebra226(2022), no. 5) requires large cardinals; it sits, implication‐wise, between Vopěnka's Principle and the existence of an ‐strongly compact cardinal.While deconstructibility of a class of modules always implies the precovering property by Saorín and Šťovíček (Adv. Math.228(2011), no. 2, 968–1007), the concepts are (consistently) nonequivalent, even for classes of abelian groups closed under extensions, homomorphic images, and colimits. 
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  2. ; ; ; (, Journal of Mathematical Logic)
    We address the question of consistency strength of certain filters and ultrafilters which fail to satisfy the Galvin property. We answer questions [Benhamou and Gitik, Ann. Pure Appl. Logic 173 (2022) 103107; Questions 7.8, 7.9], [Benhamou et al., J. Lond. Math. Soc. 108(1) (2023) 190–237; Question 5] and improve theorem [Benhamou et al., J. Lond. Math. Soc. 108(1) (2023) 190–237; Theorem 2.3]. 
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