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

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)

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.

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.

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)

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)

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)

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.

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.

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 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.

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 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.

We consider random processes more general than those considered by Erdös and Rényi for generating the countable random graph. It is proved that, in the category sense, almost all random processes we consider generate the countable random graph with probability 1. Under a weak boundedness assumption we give a criterion for the random processes which generate the countable random graph almost surely. We also consider further questions asked by Jackson regarding the outcome graphs when the process fails to produce the (...) countable random graph. (shrink)