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).

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 (...) 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 under Borel reducibility, but in fact any analytic equivalence relation is Borel equivalent to such a relation. This result and the techniques introduced answer questions raised in [5] about the comparison between isomorphism and bi-embeddability. Finally, as in [5] our results apply not only to classes of countable structures defined by sentences of ω ₁ ω , but also to discrete metric or ultrametric Polish spaces, compact metrizable topological spaces and separable Banach spaces, with various notions of embeddability appropriate for these classes, as well as to actions of Polish monoids. (shrink)

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).

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 (...) groups. This fully generalizes to the uncountable case the main results of [A. Louveau and C. Rosendal, Complete analytic equivalence relations, Trans. Amer. Math. Soc.357(12) (2005) 4839–4866; S.-D. Friedman and L. Motto Ros, Analytic equivalence relations and bi-embeddability, J. Symbolic Logic76(1) (2011) 243–266; J. Williams, Universal countable Borel quasi-orders, J. Symbolic Logic79(3) (2014) 928–954; F. Calderoni and L. Motto Ros, Universality of group embeddability, Proc. Amer. Math. Soc.146 (2018) 1765–1780]. (shrink)

Film clips are proven to be one of the most efficient techniques in emotional induction. However, there is scant literature on the effect of this procedure in older adults and, specifically, the effect of using different positive stimuli. Thus, the aim of the present study was to examine emotional differences between young and older adults and to know how a set of film clips works as mood induction procedure in older adults, especially, when trying to elicit attachment-related emotions. To this (...) end, we use this procedure to analyze differences in subjective emotional response between young and older adults. A sample of 57 older adults and 83 young adults watched a film set previously validated in young population. Their responses were studied in an individual laboratory session to elicit 6 target emotions (disgust, fear, sadness, anger, amusement and tenderness) and neutral state. Self-reported emotional experience was measured using the Self-Assessment Manikin (SAM). Our results show that film clips are capable of evoking positive and negative emotions in older adults. Furthermore, older adults experienced more intensely negative emotions than young adults, especially in response to disgust and fear clips. They also reported higher arousal than young adults, especially in the case of sadness, anger and tenderness clips. Nevertheless, the older adults recovered more easily from the effects of the emotion induction. The young adults reported higher arousal ratings than older adults in response to amusement film clips. On the other hand, this study reflects the importance of controlling the baseline state to study the real strength of mood induction. Overall, current data suggests significant differences occur in emotional response in adult age and that film clips are an effective tool for studying positive and negative emotions in aging research. (shrink)