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Daniel Palacín [8]D. Palacín [1]
  1.  7
    On Superstable Expansions of Free Abelian Groups.Daniel Palacín & Rizos Sklinos - 2018 - Notre Dame Journal of Formal Logic 59 (2):157-169.
    We prove that has no proper superstable expansions of finite Lascar rank. Nevertheless, this structure equipped with a predicate defining powers of a given natural number is superstable of Lascar rank ω. Additionally, our methods yield other superstable expansions such as equipped with the set of factorial elements.
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  2.  11
    On $N$ -Dependence.Artem Chernikov, Daniel Palacin & Kota Takeuchi - 2019 - Notre Dame Journal of Formal Logic 60 (2):195-214.
    In this article, we develop and clarify some of the basic combinatorial properties of the new notion of n-dependence recently introduced by Shelah. In the same way as dependence of a theory means its inability to encode a bipartite random graph with a definable edge relation, n-dependence corresponds to the inability to encode a random -partite -hypergraph with a definable edge relation. We characterize n-dependence by counting φ-types over finite sets, and in terms of the collapse of random ordered -hypergraph (...)
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  3.  8
    Generalized Amalgamation and Homogeneity.Daniel Palacín - 2017 - Journal of Symbolic Logic 82 (4):1409-1421.
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  4.  17
    Ample Thoughts.Daniel Palacín & Frank O. Wagner - 2013 - Journal of Symbolic Logic 78 (2):489-510.
    Non-$n$-ampleness as defined by Pillay [20] and Evans [5] is preserved under analysability. Generalizing this to a more general notion of $\Sigma$-ampleness, this gives an immediate proof for all simple theories of a weakened version of the Canonical Base Property (CBP) proven by Chatzidakis [4] for types of finite SU-rank. This is then applied to the special case of groups.
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  5.  6
    On the Class of Flat Stable Theories.Daniel Palacín & Saharon Shelah - 2018 - Annals of Pure and Applied Logic 169 (8):835-849.
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  6.  18
    On Omega-Categorical Simple Theories.Daniel Palacín - 2012 - Archive for Mathematical Logic 51 (7-8):709-717.
    In the present paper we shall prove that countable ω-categorical simple CM-trivial theories and countable ω-categorical simple theories with strong stable forking are low. In addition, we observe that simple theories of bounded finite weight are low.
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  7.  1
    The Dp-Rank of Abelian Groups.Yatir Halevi & Daniel Palacín - 2019 - Journal of Symbolic Logic 84 (3):957-986.
    An equation to compute the dp-rank of any abelian group is given. It is also shown that its dp-rank, or more generally that of any one-based group, agrees with its Vapnik–Chervonenkis density. Furthermore, strong abelian groups are characterised to be precisely those abelian groups A such that there are only finitely many primes p such that the group A / pA is infinite and for every prime p, there are only finitely many natural numbers n such that $\left[p]/\left[p]$ is infinite.Finally, (...)
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  8.  16
    Elimination of Hyperimaginaries and Stable Independence in Simple CM-Trivial Theories.D. Palacín & F. O. Wagner - 2013 - Notre Dame Journal of Formal Logic 54 (3-4):541-551.
    In a simple CM-trivial theory every hyperimaginary is interbounded with a sequence of finitary hyperimaginaries. Moreover, such a theory eliminates hyperimaginaries whenever it eliminates finitary hyperimaginaries. In a supersimple CM-trivial theory, the independence relation is stable.
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  9.  6
    On Definable Galois Groups and the Strong Canonical Base Property.Daniel Palacín & Anand Pillay - 2017 - Journal of Mathematical Logic 17 (1):1750002.
    In [E. Hrushovski, D. Palacín and A. Pillay, On the canonical base property, Selecta Math. 19 865–877], Hrushovski and the authors proved, in a certain finite rank environment, that rigidity of definable Galois groups implies that [Formula: see text] has the canonical base property in a strong form; “internality to” being replaced by “algebraicity in”. In the current paper, we give a reasonably robust definition of the “strong canonical base property” in a rather more general finite rank context than [E. (...)
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