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  1.  17
    Set-Theoretic Blockchains.Miha E. Habič, Joel David Hamkins, Lukas Daniel Klausner, Jonathan Verner & Kameryn J. Williams - 2019 - Archive for Mathematical Logic 58 (7-8):965-997.
    Given a countable model of set theory, we study the structure of its generic multiverse, the collection of its forcing extensions and ground models, ordered by inclusion. Mostowski showed that any finite poset embeds into the generic multiverse while preserving the nonexistence of upper bounds. We obtain several improvements of his result, using what we call the blockchain construction to build generic objects with varying degrees of mutual genericity. The method accommodates certain infinite posets, and we can realize these embeddings (...)
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  2.  13
    Cichoń’s diagram and localisation cardinals.Martin Goldstern & Lukas Daniel Klausner - 2021 - Archive for Mathematical Logic 60 (3):343-411.
    We reimplement the creature forcing construction used by Fischer et al. :1045–1103, 2017. https://doi.org/10.1007/S00153-017-0553-8. arXiv:1402.0367 [math.LO]) to separate Cichoń’s diagram into five cardinals as a countable support product. Using the fact that it is of countable support, we augment our construction by adding uncountably many additional cardinal characteristics, sometimes referred to as localisation cardinals.
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  3. “Computer Says No”: Algorithmic Decision Support and Organisational Responsibility.Angelika Adensamer, Rita Gsenger & Lukas Daniel Klausner - 2021 - Journal of Responsible Technology 7:100014.
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  4. Many different uniformity numbers of Yorioka ideals.Lukas Daniel Klausner & Diego Alejandro Mejía - 2022 - Archive for Mathematical Logic 61 (5):653-683.
    Using a countable support product of creature forcing posets, we show that consistently, for uncountably many different functions the associated Yorioka ideals’ uniformity numbers can be pairwise different. In addition we show that, in the same forcing extension, for two other types of simple cardinal characteristics parametrised by reals, for uncountably many parameters the corresponding cardinals are pairwise different.
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  5.  5
    Creatures and Cardinals.Lukas Daniel Klausner - 2019 - Bulletin of Symbolic Logic 25 (2):218-219.