We show that for any ω-r.e. degree d and n-r.e. degree b with d

Mathematical Logic in Philosophy of Mathematics

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As an important corporate governance mechanism, directors’ and officers’ liability insurance is theoretically associated with corporate financialization because it directly affects incentive constraints and risk preference of enterprise managers. However, whether there is a causal relationship in fact has not been sufficiently empirically investigated. Using a sample of Chinese non-financial listed companies in Shanghai and Shenzhen A-shares from 2008 to 2020, this paper empirically analyzes how corporate subscription to directors’ and officers’ liability insurance affects corporate financialization and examines the mediating (...) role played by risk-taking, financing constraints, and audit quality. The study finds that corporate subscription to D&O insurance increases corporate financialization. In terms of the influential mechanism, subscription to D&O insurance promotes financialization by increasing risk-taking, alleviating financing constraints, and improving audit quality. In addition, the results in the heterogeneity analysis suggest that the promotion of financialization by subscribing to D&O insurance is more significant in state-owned enterprises, growth and decline stage enterprises, and non-dual-employment enterprises. (shrink)

The Turing degrees of infinite levels of the Ershov hierarchy were studied by Liu and Peng [8]. In this paper, we continue the study of Turing degrees of infinite levels and lift the study of density property to the levels beyond ω2. In doing so, we rely on notations with some nice properties. We introduce the concept of normalizing notations and generate normalizing notations for higher levels. The generalizations of the weak density theorem and the nondensity theorem are proved for (...) higher levels in the Ershov hierarchy. Furthermore, we also investigate the minimal degrees in the infinite levels of the Ershov hierarchy. (shrink)

Theoretical researchers of manager psychology have excellent potential to extend its research framework to more enterprise application areas, such as innovation, performance, and safety in production. Research in these areas has also been increasing in the past 10 years. Psychological capital is composed of four aspects: self-efficacy, hope, optimism, and tenacity. It plays an essential role in stimulating organizational growth and improving organizational performance. In safety management work, managers, as the core members of the organization, have a relationship between their (...) psychological capital and employees’ safety performance. Nevertheless, the closeness of the relationship between psychological capital and employee safety performance has not been fully demonstrated by academic circles. Based on positive psychology theory, this paper conducts a questionnaire survey of 157 managers and 314 employees related to safety work in manufacturing enterprises. From the new perspective of organizational emotional capability, this paper investigates the complex and extensive social-psychological role in organizations and combs, analyzes, and integrates relevant psychological research to construct the influence mechanism of managers’ psychological capital and employee safety performance. Finally, the three important issues found based on data analysis were: Managers’ psychological capital has a significant positive impact both on employee safety performance and organizational emotional capability; Organizational emotional capability has a significant positive impact on employee safety performance; organizational emotional capability plays a partial mediating role in the relationship between managers’ psychological capital and employee safety performance. (shrink)

In this thesis, we study Turing degrees in the context of classical recursion theory. What we are interested in is the partially ordered structures $\mathcal {D}_{\alpha }$ for ordinals $\alpha <\omega ^2$ and $\mathcal {D}_{a}$ for notations $a\in \mathcal {O}$ with $|a|_{o}\geq \omega ^2$.The dissertation is motivated by the $\Sigma _{1}$ -elementary substructure problem: Can one structure in the following structures $\mathcal {R}\subsetneqq \mathcal {D}_{2}\subsetneqq \dots \subsetneqq \mathcal {D}_{\omega }\subsetneqq \mathcal {D}_{\omega +1}\subsetneqq \dots \subsetneqq \mathcal {D}$ be a $\Sigma _{1}$ (...) -elementary substructure of another? For finite levels of the Ershov hierarchy, Cai, Shore, and Slaman [Journal of Mathematical Logic, vol. 12, p. 1250005] showed that $\mathcal {D}_{n}\npreceq _{1}\mathcal {D}_{m}$ for any $n < m$. We consider the problem for transfinite levels of the Ershov hierarchy and show that $\mathcal {D}_{\omega }\npreceq _{1}\mathcal {D}_{\omega +1}$. The techniques in Chapters 2 and 3 are motivated by two remarkable theorems, Sacks Density Theorem and the d.r.e. Nondensity Theorem.In Chapter 1, we first briefly review the background of the research areas involved in this thesis, and then review some basic definitions and classical theorems. We also summarize our results in Chapter 2 to Chapter 4. In Chapter 2, we show that for any $\omega $ -r.e. set D and r.e. set B with $D<_{T}B$, there is an $\omega +1$ -r.e. set A such that $D<_{T}A<_{T}B$. In Chapter 3, we show that for some notation a with $|a|_{o}=\omega ^{2}$, there is an incomplete $\omega +1$ -r.e. set A such that there are no a-r.e. sets U with $A<_{T}U<_{T}K$. In Chapter 4, we generalize above results to higher levels. We investigate Lachlan sets and minimal degrees on transfinite levels and show that for any notation a, there exists a $\Delta ^{0}_{2}$ -set A such that A is of minimal degree and $A\not \equiv _T U$ for all a-r.e. sets U.prepared by Cheng Peng.E-mail: [email protected]. (shrink)