6 found
Order:
  1.  27
    Baire Reductions and Good Borel Reducibilities.Luca Motto Ros - 2010 - Journal of Symbolic Logic 75 (1):323-345.
    In [9] we have considered a wide class of "well-behaved" reducibilities for sets of reals. In this paper we continue with the study of Borel reducibilities by proving a dichotomy theorem for the degree-structures induced by good Borel reducibilities. This extends and improves the results of [9] allowing to deal with a larger class of notions of reduction (including, among others, the Baire class ξ functions).
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  2.  7
    Analytic Equivalence Relations and Bi-Embeddability.Sy-David Friedman & Luca Motto Ros - 2011 - Journal of Symbolic Logic 76 (1):243-266.
    Louveau and Rosendal [5] have shown that the relation of bi-embeddability for countable graphs as well as for many other natural classes of countable structures is complete under Borel reducibility for analytic equivalence relations. This is in strong contrast to the case of the isomorphism relation, which as an equivalence relation on graphs is far from complete.In this article we strengthen the results of [5] by showing that not only does bi-embeddability give rise to analytic equivalence relations which are complete (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  3.  11
    Borel-Amenable Reducibilities for Sets of Reals.Luca Motto Ros - 2009 - Journal of Symbolic Logic 74 (1):27-49.
    We show that if Ƒ is any "well-behaved" subset of the Borei functions and we assume the Axiom of Determinacy then the hierarchy of degrees on $P(^\omega \omega )$ induced by Ƒ turns out to look like the Wadge hierarchy (which is the special case where Ƒ is the set of continuous functions).
    Direct download (9 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  4.  9
    On the Structure of Finite Level and Ω-Decomposable Borel Functions.Luca Motto Ros - 2013 - Journal of Symbolic Logic 78 (4):1257-1287.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  5.  6
    Analytic Equivalence Relations and Bi-Embeddability.Sy-David Friedman & Luca Motto Ros - 2011 - Journal of Symbolic Logic 76 (1):243 - 266.
    Louveau and Rosendal [5] have shown that the relation of bi-embeddability for countable graphs as well as for many other natural classes of countable structures is complete under Borel reducibility for analytic equivalence relations. This is in strong contrast to the case of the isomorphism relation, which as an equivalence relation on graphs (or on any class of countable structures consisting of the models of a sentence of L ω ₁ ω ) is far from complete (see [5, 2]). In (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  6.  3
    Uncountable Structures Are Not Classifiable Up to Bi-Embeddability.Filippo Calderoni, Heike Mildenberger & Luca Motto Ros - 2019 - Journal of Mathematical Logic 20 (1):2050001.
    Answering some of the main questions from [L. Motto Ros, The descriptive set-theoretical complexity of the embeddability relation on models of large size, Ann. Pure Appl. Logic164(12) (2013) 1454–1492], we show that whenever κ is a cardinal satisfying κ<κ=κ>ω, then the embeddability relation between κ-sized structures is strongly invariantly universal, and hence complete for (κ-)analytic quasi-orders. We also prove that in the above result we can further restrict our attention to various natural classes of structures, including (generalized) trees, graphs, or (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark