We study computably enumerable equivalence relations (ceers) on N and unravel a rich structural theory for a strong notion of reducibility among ceers.

Significant research has been conducted on the influence of entrepreneurial intention on entrepreneurial education and entrepreneurship practice. Similarly, this study aims to explore how creativity plays a mediating role in the influence of personality traits on entrepreneurial intention. As many as 674 valid questionnaires were collected from college students in China, allowing the relationship between personality traits, creativity, and entrepreneurial intention to be analyzed in detail. The following results are found through a series of explorations. First, neuroticism in personality traits (...) has a significant negative impact on entrepreneurial intention, while conscientiousness, openness, and extraversion have a significant positive impact. Second, neuroticism has a significant negative impact on creativity, while conscientiousness, openness, and extraversion have a significant positive impact. Third, creativity has a significant positive impact on entrepreneurial intention, it has a partial mediating role between neuroticism, conscientiousness, extraversion, and entrepreneurial intention along with a complete mediating role between openness and entrepreneurial intention. The research results further provide a reference value for the improvement and optimization of entrepreneurial practice. (shrink)

In this paper we study a notion of HL-extension for a structure in a finite relational language $\mathcal {L}$. We give a description of all finite minimal HL-extensions of a given finite $\mathcal {L}$ -structure. In addition, we study a group-theoretic property considered by Herwig–Lascar and show that it is closed under taking free products. We also introduce notions of coherent extensions and ultraextensive $\mathcal {L}$ -structures and show that every countable $\mathcal {L}$ -structure can be extended to a countable (...) ultraextensive structure. Finally, it follows from our results that the automorphism group of any countable ultraextensive $\mathcal {L}$ -structure has a dense locally finite subgroup. (shrink)

Exploring the factors influencing entrepreneurial intention is crucial to entrepreneurial practice and education. For a comprehensive understanding of the influence of narcissistic personality on entrepreneurial intention, this study analyzed the relationship between narcissistic personality, entrepreneurial self-efficacy, and entrepreneurial intention in college students sampled from three higher vocational colleges in Beijing, China. A total of 252 valid questionnaires were collected. The results show that the narcissistic personality of the college students has a significant positive effect on entrepreneurial intention and entrepreneurial self-efficacy. (...) Entrepreneurial self-efficacy of the college students has a significant positive effect on entrepreneurial intention and plays a partial mediation role in the relationship between narcissistic personality and entrepreneurial intention. Thus, the study results provide some reference for further improving entrepreneurial practice and education. (shrink)

§ 1. Introduction. In this communication we present some recent results on the classification of Polish metric spaces up to isometry and on the isometry groups of Polish metric spaces. A Polish metric space is a complete separable metric space.Our first goal is to determine the exact complexity of the classification problem of general Polish metric spaces up to isometry. This work was motivated by a paper of Vershik [1998], where he remarks : “The classification of Polish spaces up to (...) isometry is an enormous task. More precisely, this classification is not ‘smooth’ in the modern terminology.” Our Theorem 2.1 below quantifies precisely the enormity of this task.After doing this, we turn to special classes of Polish metric spaces and investigate the classification problems associated with them. Note that these classification problems are in principle no more complicated than the general one above. However, the determination of their exact complexity is not necessarily easier.The investigation of the classification problems naturally leads to some interesting results on the groups of isometries of Polish metric spaces. We shall also present these results below.The rest of this section is devoted to an introduction of some basic ideas of a theory of complexity for classification problems, which will help to put our results in perspective. Detailed expositions of this general theory can be found, e.g., in Hjorth [2000], Kechris [1999], [2001]. (shrink)

Strengthening a theorem of D.W. Kueker, this paper completely characterizes which countable structures do not admit uncountable L ω 1 ω -elementarily equivalent models. In particular, it is shown that if the automorphism group of a countable structure M is abelian, or even just solvable, then there is no uncountable model of the Scott sentence of M. These results arise as part of a study of Polish groups with compatible left-invariant complete metrics.

We consider the equivalence relations on induced by the Banach subspaces. We show that if, then there is no Borel reduction from the equivalence relation, where X is a Banach space, to.

The research aims to explore the influence mechanism of proactive personality on the entrepreneurial intentions of college students. Adopting proactive personality scale, social capital scale, human capital scale, and entrepreneurial intention scale, this research tested valid samples of 300 Chinese college students. The results revealed that proactive personality exerted a significant and positive impact on the entrepreneurial intentions. Social capital played a partial mediating role between the proactive personality and the entrepreneurial intentions. Human capital also played a partial mediating role (...) between proactive personality and entrepreneurial intentions. Social capital and human capital exerted a chain mediation effect between proactive personality and entrepreneurial intentions. The result of this research offers valuable insights to the study of the influence of college students’ proactive personality on entrepreneurial intentions and provides entrepreneurship education management in colleges with specific practical suggestions so as to improve entrepreneurial intentions among college students. (shrink)

The present study explored the correlation between music preference and mental health of college students to make an empirical contribution to research in this field. The self-reported music preference scale and positive mental health scale of college students were adopted to conduct a questionnaire survey in college students. Common method variance was conducted to test any serious common method bias problem. No serious common method bias problem was observed. The results showed that college students’ preference for pop music, Western classical (...) music, and Chinese traditional music has a significant and positive correlation with their mental health. Furthermore, college students’ preference for heavy music has a significant and inverse correlation with their mental health. This research presents a correlational study; therefore, no causality can be inferred. (shrink)

ObjectiveTo compare techniques for computing clustering and switching scores in terms of agreement, correlation, and empirical value as predictors of incident cognitive impairment.MethodsWe transcribed animal and letter F fluency recordings on 640 cases of ICI and matched controls from a national epidemiological study, amending each transcription with word timings. We then calculated clustering and switching scores, as well as scores indexing speed of responses, using techniques described in the literature. We evaluated agreement among the techniques with Cohen’s κ and calculated (...) correlations among the scores. After fitting a base model with raw scores, repetitions, and intrusions, we fit a series of Bayesian logistic regression models adding either clustering and switching scores or speed scores, comparing the models in terms of several metrics. We partitioned the ICI cases into acute and progressive cases and repeated the regression analysis for each group.ResultsFor animal fluency, we found that models with speed scores derived using the slope difference algorithm achieved the best values of the Watanabe–Akaike Information Criterion, but with good net reclassification improvement only for the progressive group. For letter fluency, different models excelled for prediction of acute and progressive cases. For acute cases, NRI was best for speed scores derived from a network model, while for progressive cases, the best model used clustering and switching scores derived from the same network model. Combining variables from the best animal and letter F models led to marginal improvements in model fit and NRI only for the all-cases and acute-cases analyses.ConclusionSpeed scores improve a base model for predicting progressive cognitive impairment from animal fluency. Letter fluency scores may provide complementary information. (shrink)

Strengthening known instances of Vaught Conjecture, we prove the Glimm-Effros dichotomy theorems for countable linear orderings and for simple trees. Corollaries of the theorems answer some open questions of Friedman and Stanley in an L ω 1ω -interpretability theory. We also give a survey of this theory.

We prove that the strong Martin conjecture is false. The counterexample is the first-order theory of infinite atomic Boolean algebras. We show that for this class of Boolean algebras, the classification of their (ω + ω)-elementary theories can be reduced to the classification of the elementary theories of their quotient algebras modulo the Frechet ideals.

We prove a number of results about countable Borel equivalence relations with forcing constructions and arguments. These results reveal hidden regularity properties of Borel complete sections on certain orbits. As consequences they imply the nonexistence of Borel complete sections with certain features.

We study the notion of polynomial-time relation reducibility among computable equivalence relations. We identify some benchmark equivalence relations and show that the reducibility hierarchy has a rich structure. Specifically, we embed the partial order of all polynomial-time computable sets into the polynomial-time relation reducibility hierarchy between two benchmark equivalence relations Eλ and id. In addition, we consider equivalence relations with finitely many nontrivial equivalence classes and those whose equivalence classes are all finite.

In this paper we define and study conditional problems and their degrees. The main result is that the class of conditional degrees is a lattice extending the ordinary Turing degrees and it is dense. These properties are not shared by ordinary Turing degrees. We show that the class of conditional many-one degrees is a distributive lattice. We also consider properties of semidecidable problems and their degrees, which are analogous to r.e. sets and degrees.

Let E be a coanalytic equivalence relation on a Polish space X and (A n ) n∈ω a sequence of analytic subsets of X. We prove that if lim sup n∈K A n meets uncountably many E-equivalence classes for every K ∈ [ω] ω , then there exists a K ∈ [ω] ω such that ⋂ n∈K A n contains a perfect set of pairwise E-inequivalent elements.

This study aimed to explore the psychological mechanisms behind the relationship between kindergarten parental satisfaction and parental loyalty. This study used the parental satisfaction scale, parental trust scale, parental relationship commitment scale, and parental loyalty scale on 923 kindergarten parents. The test was conducted on 923 kindergarten parents. The results of this study showed that parental satisfaction significantly and positively affected parental loyalty. Parental trust was partially mediated between parental satisfaction and parental loyalty. Parental relationship commitment was also partially mediated (...) between parental satisfaction and parental loyalty. Regarding to parental satisfaction and parental loyalty, parental trust and parental relationship commitment had chain mediation effect between parental satisfaction and parental loyalty. The findings of this study provided valuable insights into the effect of parental satisfaction on parental loyalty and offer concrete practical suggestions for kindergarten operators to improve the loyalty of kindergarten parents. (shrink)

We investigate diagonal actions of Polish groups and the related intersection operator on closed subgroups of the acting group. The Borelness of the diagonal orbit equivalence relation is characterized and is shown to be connected with the Borelness of the intersection operator. We also consider relatively tame Polish groups and give a characterization of them in the class of countable products of countable abelian groups. Finally an example of a logic action is considered and its complexity in the Borel reducbility (...) hierarchy determined. (shrink)

We define some variations of the Scott rank for countable models and obtain some inequalities involving the ranks. For mono-unary algebras we prove that the game rank of any subtree does not exceed the game rank of the whole model. However, similar questions about linear orders remain unresolved.