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  1.  8
    Linear Orders: When Embeddability and Epimorphism Agree.Riccardo Camerlo, Raphaël Carroy & Alberto Marcone - 2019 - Journal of Mathematical Logic 19 (1):1950003.
    When a linear order has an order preserving surjection onto each of its suborders, we say that it is strongly surjective. We prove that the set of countable strongly surjective linear orders is a [Formula: see text]-complete set. Using hypotheses beyond ZFC, we prove the existence of uncountable strongly surjective orders.
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  2.  11
    Finiteness Axioms on Fragments of Intuitionistic Set Theory.Riccardo Camerlo - 2007 - Notre Dame Journal of Formal Logic 48 (4):473-488.
    It is proved that in a suitable intuitionistic, locally classical, version of the theory ZFC deprived of the axiom of infinity, the requirement that every set be finite is equivalent to the assertion that every ordinal is a natural number. Moreover, the theory obtained with the addition of these finiteness assumptions is equivalent to a theory of hereditarily finite sets, developed by Previale in "Induction and foundation in the theory of hereditarily finite sets." This solves some problems stated there. The (...)
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  3.  23
    Coloring Linear Orders with Rado's Partial Order.Riccardo Camerlo & Alberto Marcone - 2007 - Mathematical Logic Quarterly 53 (3):301-305.
    Let ⪯R be the preorder of embeddability between countable linear orders colored with elements of Rado's partial order . We show that ⪯R has fairly high complexity with respect to Borel reducibility , although its exact classification remains open.
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  4.  7
    Polish Metric Spaces with Fixed Distance Set.Riccardo Camerlo, Alberto Marcone & Luca Motto Ros - 2020 - Annals of Pure and Applied Logic 171 (10):102832.
    We study Polish spaces for which a set of possible distances $A \subseteq R^+$ is fixed in advance. We determine, depending on the properties of A, the complexity of the collection of all Polish metric spaces with distances in A, obtaining also example of sets in some Wadge classes where not many natural examples are known. Moreover we describe the properties that A must have in order that all Polish spaces with distances in that set belong to a given class, (...)
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  5.  8
    Some Remarks on Baire’s Grand Theorem.Riccardo Camerlo & Jacques Duparc - 2018 - Archive for Mathematical Logic 57 (3-4):195-201.
    We provide a game theoretical proof of the fact that if f is a function from a zero-dimensional Polish space to \ that has a point of continuity when restricted to any non-empty compact subset, then f is of Baire class 1. We use this property of the restrictions to compact sets to give a generalisation of Baire’s grand theorem for functions of any Baire class.
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  6.  19
    The Relation of Recursive Isomorphism for Countable Structures.Riccardo Camerlo - 2002 - Journal of Symbolic Logic 67 (2):879-895.
    It is shown that the relations of recursive isomorphism on countable trees, groups, Boolean algebras, fields and total orderings are universal countable Borel equivalence relations, thus providing a countable analogue of the Borel completeness of the isomorphism relations on these same classes. I.
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