In this paper, we study the bi-isolation phenomena in the d.c.e. degrees and prove that there are c.e. degrees c₁ < c₂ and a d.c.e. degree d ∈ (c₁, c₂) such that (c₁, d) and (d, c₂) contain no c.e. degrees. Thus, the c.e. degrees between c₁ and c₂ are all incomparable with d. We also show that there are d.c.e. degrees d₁ < d₂ such that (d₁, d₂) contains a unique c.e. degree.

In [9]. Yates proved the existence of a Turing degree a such that 0. 0′ are the only c.e. degrees comparable with it. By Slaman and Steel [7], every degree below 0′ has a 1-generic complement, and as a consequence. Yates degrees can be 1-generic, and hence can be low. In this paper, we prove that Yates degrees occur in every jump class.

Say that a d.c.e. degree d is nonisolated if for any c.e. degree a

Logic and Philosophy of Logic

Logic and Philosophy of Logic, Miscellaneous in Logic and Philosophy of Logic

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Say that a d.c.e. degree d is isolated by a c.e. degree b, if bMathematics Subject Classification (2000): 03D25, 03D30, 03D35 RID=""ID="" Key words or phrases: Computably enumerable (...) set – d.c.e. degree – Isolation – High/low hierarchy RID=""ID="" Ishmukhametov's research is supported by RFBR grant 01-01-00733, and Wu's research is supported by the Marsden Fund of New Zealand. Wu would like to thank his supervisor, Prof. Rod Downey, for his many helpful suggestions and comments. (shrink)

We show the existence of a high d. c. e. degree d and a low2 c.e. degree a such that d is isolated by a.

Say that (a, d) is an isolation pair if a is a c.e. degree, d is a d.c.e. degree, a < d and a bounds all c.e. degrees below d. We prove that there are an isolation pair (a, d) and a c.e. degree c such that c is incomparable with a, d, and c cups d to o', caps a to o. Thus, {o, c, d, o'} is a diamond embedding, which was first proved by Downey in [9]. Furthermore, (...) combined with Harrington-Soare continuity of capping degrees, our result gives an alternative proof of N5 embedding. (shrink)

In this paper, we solve a long-standing open question, about the spectrum of the successivity relation on a computable linear ordering. We show that if a computable linear ordering [Formula: see text] has infinitely many successivities, then the spectrum of the successivity relation is closed upwards in the computably enumerable Turing degrees. To do this, we use a new method of constructing [Formula: see text]-isomorphisms, which has already found other applications such as Downey, Kastermans and Lempp [9] and is of (...) independent interest. It would seem to promise many further applications. (shrink)

Cooper proved in [S.B. Cooper, Strong minimal covers for recursively enumerable degrees, Math. Logic Quart. 42 191–196] the existence of a c.e. degree with a strong minimal cover . So is the greastest c.e. degree below . Cooper and Yi pointed out in [S.B. Cooper, X. Yi, Isolated d.r.e. degrees, University of Leeds, Dept. of Pure Math., 1995. Preprint] that this strongly minimal cover cannot be d.c.e., and meanwhile, they proposed the notion of isolated degrees: a d.c.e. degree is isolated (...) by a c.e. degree if is the greatest c.e. degree below , and we also say that isolates . In [G. Wu, Bi-isolation in the d.c.e. degrees, J. Symbolic Logic 69 409–420], Wu extended Cooper–Yi’s notion and proved that there are intervals of d.c.e. degrees containing exactly one c.e. degree . Following Cooper and Yi’s notion, is called a bi-isolating degree. The bi-isolating degrees are dense in the high c.e. degrees. Arslanov asked whether the bi-isolating degrees occur in every jump class. In this paper, we prove that there are low bi-isolating degrees, providing a partial solution to Arslanov’s question. (shrink)

Say a set Gω is 1-generic if for any eω, there is a string σG such that {e}σ↓ or τσ↑). It is known that can be split into two 1-generic degrees. In this paper, we generalize this and prove that any nonzero computably enumerable degree can be split into two 1-generic degrees. As a corollary, no two computably enumerable degrees bound the same class of 1-generic degrees.

We give a characterization of strongly compact cardinals in terms of Q κ λ. We also prove that weakly normal Q-measures on Q κ λ are ⊂κ-normal.

Say that a nonzero c. e. degree b is a quasi-complement of a c. e. degree a if a ∩ b = 0 and a ∪ b is high. It is well-known that each cappable degree has a high quasi-complement. However, by the existence of the almost deep degrees, there are nonzero cappable degrees having no low quasi-complements. In this paper, we prove that any nonzero cappable degree has a low2 quasi-complement.

Say that α is an n-strongly c. e. real if α is a sum of n many strongly c. e. reals, and that α is regular if α is n-strongly c. e. for some n. Let Sn be the set of all n-strongly c. e. reals, Reg be the set of regular reals and CE be the set of c. e. reals. Then we have: S1 ⊂ S2 ⊂ · · · ⊂ Sn ⊂ · · · ⊂ ⊂ Reg (...) ⊂ CE. This gives a hierarchy of the c. e. reals. We also study the regularity of the d. c. e. reals. (shrink)

Given a d.c.e. degree d, consider the d.c.e. sets in d and the corresponding degrees of their Lachlan sets. Ishmukhametov provided a systematic investigation of such degrees, and proved that for a given d.c.e. degree d > 0, the class of its c.e. predecessors in which d is c.e., denoted as R[d], can consist of either just one element, or an interval of c.e. degrees. After this, Ishmukhametov asked whether there exists a d.c.e. degree d for which the class R[d] (...) has no minimal element. We give a positive answer to this question. (shrink)

Lachlan observed that the infimum of two r.e. degrees considered in the r.e. degrees coincides with the one considered in the ${\Delta_2^0}$ degrees. It is not true anymore for the d.r.e. degrees. Kaddah proved in (Ann Pure Appl Log 62(3):207–263, 1993) that there are d.r.e. degrees a, b, c and a 3-r.e. degree x such that a is the infimum of b, c in the d.r.e. degrees, but not in the 3-r.e. degrees, as a < x < b, c. In (...) this paper, we extend Kaddah’s result by showing that such a structural difference occurs densely in the r.e. degrees. Our result immediately implies that the isolated 3-r.e. degrees are dense in the r.e. degrees, which was first proved by LaForte. (shrink)

We prove that for any computably enumerable degree c, if it is cappable in the computably enumerable degrees, then there is a d.c.e. degree d such that c d = 0′ and c ∩ d = 0. Consequently, a computably enumerable degree is cappable if and only if it can be complemented by a nonzero d.c.e. degree. This gives a new characterization of the cappable degrees.

In [Countable thin [Formula: see text] classes, Ann. Pure Appl. Logic 59 79–139], Cenzer, Downey, Jockusch and Shore proved the density of degrees containing members of countable thin [Formula: see text] classes. In the same paper, Cenzer et al. also proved the existence of degrees containing no members of thin [Formula: see text] classes. We will prove in this paper that the c.e. degrees containing no members of thin [Formula: see text] classes are dense in the c.e. degrees. We will (...) also prove that the c.e. degrees containing members of thin [Formula: see text] classes are dense in the c.e. degrees, improving the result of Cenzer et al. mentioned above. Thus, we obtain a new natural subclass of c.e. degrees which are both dense and co-dense in the c.e. degrees, while the other such class is the class of branching c.e. degrees 113–130] for nonbranching degrees and [T. A. Slaman, The density of infima in the recursively enumerable degrees, Ann. Pure Appl. Logic 52 155–179] for branching degrees). (shrink)

A real α is called a c. e. real if it is the halting probability of a prefix free Turing machine. Equivalently, α is c. e. if it is left computable in the sense that L = {q ∈ ℚ : q ≤ α} is a computably enumerable set. The natural field formed by the c. e. reals turns out to be the field formed by the collection of the d. c. e. reals, which are of the form α—β, where (...) α and β are c. e. reals. While c. e. reals can only be found in the c. e. degrees, Zheng has proven that there are Δ02 degrees that are not even n-c. e. for any n and yet contain d. c. e. reals, where a degree is n-c. e. if it contains an n-c. e. set. In this paper we will prove that every ω-c. e. degree contains a d. c. e. real, but there are ω + 1-c. e. degrees and, hence Δ02 degrees, containing no d. c. e. real. (shrink)

In this paper, we improve a result of Seetapun and prove that above any nonzero, incomplete recursively enumerable degree a, there is a high2 r.e. degree c>ac>a witnessing that a is locally noncappable . Theorem 1.1 provides a scheme of obtaining high2 nonboundings , as all known high2 nonboundings, such as high2 degrees bounding no minimal pairs, high2 plus-cuppings, etc.

Lachlan observed that any nonzero d.c.e. degree bounds a nonzero c.e. degree. In this paper, we study the c.e. predecessors of d.c.e. degrees, and prove that given a nonzero d.c.e. degree , there is a c.e. degree below and a high d.c.e. degree such that bounds all the c.e. degrees below . This result gives a unified approach to some seemingly unrelated results. In particular, it has the following two known theorems as corollaries: there is a low c.e. degree isolating (...) a high d.c.e. degree [S. Ishmukhametov, G. Wu, Isolation and the high/low hierarchy, Arch. Math. Logic 41 259–266]; there is a high d.c.e. degree bounding no minimal pairs [C.T. Chong, A. Li, Y. Yang, The existence of high nonbounding degrees in the difference hierarchy, Ann. Pure Appl. Logic 138 31–51]. (shrink)

Cholak, Groszek and Slaman proved in J Symb Log 66:881–901, 2001 that there is a nonzero computably enumerable (c.e.) degree cupping every low c.e. degree to a low c.e. degree. In the same paper, they pointed out that every nonzero c.e. degree can cup a low2 c.e. degree to a nonlow2 degree. In Jockusch et al. (Trans Am Math Soc 356:2557–2568, 2004) improved the latter result by showing that every nonzero c.e. degree c is cuppable to a high c.e. degree (...) by a low2 c.e. degree b. It is natural to ask in which subclass of low2 c.e. degrees can b in Jockusch et al. (Trans Am Math Soc 356:2557–2568, 2004) be located. Wu proved in Math Log Quart 50:189–201, 2004 that b can be cappable. We prove in this paper that b in Jockusch, Li and Yang’s result can be noncuppable, improving both Jockusch, Li and Yang, and Wu’s results. (shrink)

Say that an incomplete d.r.e. degree has almost universal cupping property, if it cups all the r.e. degrees not below it to 0′. In this paper, we construct such a degree d, with all the r.e. degrees not cupping d to 0′ bounded by some r.e. degree strictly below d. The construction itself is an interesting 0″′ argument and this new structural property can be used to study final segments of various degree structures in the Ershov hierarchy.

We show that there is a cuppable c.e. degree, all of whose cupping partners are high. In particular, not all cuppable degrees are${\operatorname {\mathrm {low}}}_3$-cuppable, or indeed${\operatorname {\mathrm {low}}}_n$cuppable for anyn, refuting a conjecture by Li. On the other hand, we show that one cannot improve highness to superhighness. We also show that the${\operatorname {\mathrm {low}}}_2$-cuppable degrees coincide with the array computable-cuppable degrees, giving a full understanding of the latter class.

We characterize the linear order types $\tau $ with the property that given any countable linear order $\mathcal {L}$, $\tau \cdot \mathcal {L}$ is a computable linear order iff $\mathcal {L}$ is a computable linear order, as exactly the finite nonempty order types.

The notion of superhigh computably enumerable (c.e.) degrees was first introduced by (Mohrherr in Z Math Logik Grundlag Math 32: 5–12, 1986) where she proved the existence of incomplete superhigh c.e. degrees, and high, but not superhigh, c.e. degrees. Recent research shows that the notion of superhighness is closely related to algorithmic randomness and effective measure theory. Jockusch and Mohrherr proved in (Proc Amer Math Soc 94:123–128, 1985) that the diamond lattice can be embedded into the c.e. tt-degrees preserving 0 (...) and 1 and that the two atoms can be low. In this paper, we prove that the two atoms in such embeddings can also be superhigh. (shrink)

After showing the downwards density of nonhemimaximal degrees, Downey and Stob continued to prove that the existence of a low₂, but not low, nonhemimaximal degree, and their proof uses the fact that incomplete m-topped degrees are low₂ but not low. As commented in their paper, the construction of such a nonhemimaximal degree is actually a primitive 0''' argument. In this paper, we give another construction of such degrees, which is a standard 0''-argument, much simpler than Downey and Stob's construction mentioned (...) above. (shrink)

This dissertation is highly motivated by d.r.e. Nondensity Theorem, which is interesting in two perspectives. One is that it contrasts Sacks Density Theorem, and hence shows that the structures of r.e. degrees and d.r.e. degrees are different. The other is to investigate what other properties a maximal degree can have.In Chapter 1, we briefly review the backgrounds of Recursion Theory which motivate the topics of this dissertation.In Chapter 2, we introduce the notion of $$ -cupping degree. It is closely related (...) to the notion of maximal d.r.e. degree. In fact, a $$-cupping degree is maximal d.r.e. degree. We then prove that there exists an isolated$$ -cupping degree by combining strategies for maximality and isolation with some efforts.Chapter 3 is part of a joint project with Steffen Lempp, Yiqun Liu, Keng Meng Ng, Cheng Peng, and Guohua Wu. In this chapter, we prove that any finite boolean algebra can be embedded into d.r.e. degrees as a final segment. We examine the proof of d.r.e. Nondensity Theorem and make developments to the technique to make it work for our theorem. The goal of the project is to see what lattice can be embedded into d.r.e. degrees as a final segment, as we observe that the technique has potential be developed further to produce other interesting results.prepared by Yong Liu.E-mail: liuyong0112@nju.edu.cn. (shrink)

In response to the COVID-19 pandemic, millions of students in China followed an emergency policy called “Suspending Classes without Stopping Learning” to continue their study online as schools across the country were closed. The present study examines how students adapted to learning online in these unprecedented circumstances. We aimed to explore the relationship between adaptability, academic emotion, and student engagement during COVID-19. 1,119 university students from 20 provinces participated in this longitudinal study (2 time points with a 2-week interval). The (...) results showed that adaptability (the ability to respond to changes) and student engagement are significantly positively correlated with positive academic emotion and negatively correlated with negative academic emotion. Furthermore, adaptability not only directly predicts student engagement, but also affects student engagement through the chain mediation of positive academic emotion and negative academic emotion. The results contribute to the gap in knowledge regarding changes in students’ learning in response to the outbreak. This study further explains the internal mechanisms mediating the relationship between adaptability and student engagement. It may provide references for educational researchers and universities in dampening the negative effects of COVID-19 on students’ learning by improving their adaptability and developing positive academic emotions. (shrink)

In order to address the influence of unethical leader behaviors in the form of abusive supervision on subordinates’ retaliatory responses, we meta-analytically examined the impact of abusive supervision on subordinate deviance, inclusive of the role of justice and power distance. Specifically, we investigated the mediating role of supervisory- and organizationally focused justice and the moderating role of power distance as one model explaining why and when abusive supervision is related to subordinate deviance toward supervisors and organizations. With 79 independent sample (...) studies, we found that abusive supervision was more strongly related to supervisory-focused justice, compared to organizationally focused justice perceptions, and both types of justice perceptions were related to target-similar deviance. Finally, our results showed that the negative implications of abusive supervision were stronger in lower power distance cultures compared to higher power distance cultures. (shrink)

本书内容涵盖执政党的政策与法律的关系,法的阶级性与社会性的关系,马克思主义关于法的概念和本质的基本原理,法是“理”与“力”的结合,法的作用与价值,民主与法制的关系,依法治国的治国方略以及对有关法学思潮 的评析等。.

This paper draws from the turnover and emotions literatures to explore how job embeddedness, in the context of abusive supervision, can impact job frustration, citizenship withdrawal, and employee deviance. Results indicate that employees with abusive supervisors were more likely to be frustrated with their jobs and engage in more deviance behaviors. And yet, the relationship between abusive supervision and job frustration was moderated by job embeddedness such that the relationship was weaker and negative for those higher in job embeddedness and (...) stronger and positive for those lower in job embeddedness. In other words, contrary to our original predictions, individuals who were more embedded in their jobs with an abusive supervisor were actually less likely to experience job frustration or engage deviance behaviors. Important implications for management research and practice are discussed. (shrink)

Speech recognition by second language (L2) learners in optimal and suboptimal conditions has been examined extensively with English as the target language in most previous studies. This study extended existing experimental protocols ( Wang et al., 2013 ) to investigate Mandarin speech recognition by Japanese learners of Mandarin at two different levels (elementary vs. intermediate) of proficiency. The overall results showed that in addition to L2 proficiency, semantic context, F0 contours, and listening condition all affected the recognition performance on the (...) Mandarin sentences. However, the effects of semantic context and F0 contours on L2 speech recognition diverged to some extent. Specifically, there was significant modulation effect of listening condition on semantic context, indicating that L2 learners made use of semantic context less efficiently in the interfering background than in quiet. In contrast, no significant modulation effect of listening condition on F0 contours was found. Furthermore, there was significant interaction between semantic context and F0 contours, indicating that semantic context becomes more important for L2 speech recognition when F0 information is degraded. None of these effects were found to be modulated by L2 proficiency. The discrepancy in the effects of semantic context and F0 contours on L2 speech recognition in the interfering background might be related to differences in processing capacities required by the two types of information in adverse listening conditions. (shrink)

ABSTRACT This research aims to clarify the relationship between creativity and dishonesty. Study 1 examined whether creativity primed by the scrambled sentence test could influence dishonesty. The results showed that primed individuals were less likely to act dishonestly. Study 2 investigated the association between creative style and spontaneous and instructed dishonesty. Rule-followers more often implemented spontaneous dishonest behavior but showed low accuracy in instructed lying tasks. The findings expand our understanding of the correlation between creativity and unethical behavior, which may (...) improve moral creative talents. (shrink)

According to the three-tier hierarchy of motivational potency in the self system, the self can be divided into individual self, relational self, and collective self, and individual self is at the top of the motivational hierarchy in Western culture. However, the motivational primacy of the individual self is challenged in Chinese culture, which raises the question about whether the three-tier hierarchy of motivational potency in the self system can be differentiated in the collectivist brain. The present study recorded the event-related (...) potentials (ERPs) to evaluate brain responses when participants gambled for individual self, for a close friend (relational self), or for the class (collective self). The ERP results showed that when outcome feedback was positive, gambling for individual self evoked a larger reward positivity compared with gambling for a friend or for the class, while there is no difference between the latter two conditions. In contrast, when outcome feedback was negative, no significant effect was found between conditions. The present findings provide direct electrophysiological evidence that individual self is at the top of the three-tier hierarchy of the motivational system in the collectivist brain, which supports the classical pancultural view that individual self has motivational primacy. (shrink)

Background: Independent decision-making is one of the basic rights of patients. However, in clinical practice, most older cancer patients’ treatment decisions are made by family members. Objective: This study attempted to analyze the treatment decision-making process and formation mechanism for older cancer patients within the special cultural context of Chinese medical practice. Method: A qualitative study was conducted. With the sample saturation principle, data collected by in-depth interviews with 17 family members and 12 patients were subjected to thematic analysis. Ethical (...) considerations: The study was approved by the ethics committees of Sun Yat-sen University. All participants provided verbal informed consent after being told their rights of confidentiality, anonymity, and voluntary participation. They had the right to refuse to answer questions and could withdraw at any time. Results: Three themes emerged: (1) complex process; (2) transformation of family decision-making power; and (3) individual compromise. Family members inevitably had different opinions during the long process of treatment decision-making for older cancer patients. The direction of this process could be regarded as an extension of the family power relationship. The patient usually compromised the decision to survive, which was made by family members. Conclusion: This study describes the treatment decision-making process of older cancer patients in the context of Chinese culture. The reasons underlying this process are related to the views on life and death and family values. An individual is a part of the family, which is often seen as the minimal interpersonal unit in Chinese society. It is significant that while emphasizing patient autonomy in the decision-making process, health professionals should also pay attention to the important roles of culture and family. (shrink)

Ever since the outbreak of the coronavirus disease, people have been flooded with vast amounts of information related to the virus and its social consequences. This paper draws on social amplification theory and the extended parallel process model and assesses the following: how two amplification stations—news media and peoples’ personal networks—influence the risk-related perceptions of people and how these risk-related perceptions impact people’s health-protective behaviors. This study surveyed 1,946 participants. The results indicate that peoples’ exposure to news media significantly and (...) positively predicted both perceived efficacy and perceived threat. It also shows that peoples’ exposure to risk-related information through their personal networks negatively predicted their perceived efficacy, but it positively predicted their perceived threat. The mediating effect of fear was examined, and the result was contradictory to the EPPM. In short, this study reveals the underlying mechanism of individuals’ exposure to risk information, processing, and precautionary measures. (shrink)