We study the isomorphism and bi-embeddability relations on the spaces of Kazhdan groups and finitely generated simple groups.

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)

We study the algorithmic complexity of embeddings between bi-embeddable equivalence structures. We define the notions of computable bi-embeddable categoricity, \ bi-embeddable categoricity, and degrees of bi-embeddable categoricity. These notions mirror the classical notions used to study the complexity of isomorphisms between structures. We show that the notions of \ bi-embeddable categoricity and relative \ bi-embeddable categoricity coincide for equivalence structures for \. We also prove that computable equivalence structures have degree of bi-embeddable categoricity \, or \. We furthermore obtain results (...) on the index set complexity of computable equivalence structure with respect to bi-embeddability. (shrink)

We investigate the complexity of embeddings between bi-embeddable structures. In analogy with categoricity spectra, we define the bi-embeddable categoricity spectrum of a structure A as the family of Turing degrees that compute embeddings between any computable bi-embeddable copies of A; the degree of bi-embeddable categoricity of A is the least degree in this spectrum (if it exists). We extend many known results about categoricity spectra to the case of bi-embeddability. In particular, we exhibit structures without degree of bi-embeddable categoricity, (...) and we show that every degree d.c.e above 0(α) for α a computable successor ordinal and 0(λ) for λ a computable limit ordinal is a degree of bi-embeddable categoricity. We also give examples of families of degrees that are not bi-embeddable categoricity spectra. (shrink)

We study the algorithmic complexity of isomorphic embeddings between computable structures.

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)

We show that if κ is a weakly compact cardinal then the embeddability relation on trees of size κ is invariantly universal. This means that for every analytic quasi-order R on the generalized Cantor space View the MathML source there is an Lκ+κ-sentence φ such that the embeddability relation on its models of size κ, which are all trees, is Borel bi-reducible to R. In particular, this implies that the relation of embeddability on trees of size κ (...) is complete for analytic quasi-orders on View the MathML source. These facts generalize analogous results for κ=ω obtained in Louveau and Rosendal [17] and Friedman and Motto Ros [6], and it also partially extends a result from Baumgartner [3] concerning the structure of the embeddability relation on linear orders of size κ. (shrink)

We study the bi-embeddability and elementary bi-embeddability relation on graphs under Borel reducibility and investigate the degree spectra realized by these relations. We first give a Borel reduction from embeddability on graphs to elementary embeddability on graphs. As a consequence we obtain that elementary bi-embeddability on graphs is a $\boldsymbol {\Sigma }^1_1$ complete equivalence relation. We then investigate the algorithmic properties of this reduction. We obtain that elementary bi-embeddability on the class of computable graphs (...) is $\Sigma ^1_1$ complete with respect to computable reducibility and show that the elementary bi-embeddability and bi-embeddability spectra realized by graphs are related. (shrink)

We show that if a countable structure M in a finite relational language is not cellular, then there is an age-preserving $N \supseteq M$ such that $2^{\aleph _0}$ many structures are bi-embeddable with N. The proof proceeds by a case division based on mutual algebraicity.

A complete theory T has the Schröder–Bernstein property or simply the SB-property if any pair of elementarily bi-embeddable models are isomorphic. This property has been studied in the discrete first-order setting and can be seen as a first step towards classification theory. This paper deals with the SB-property on continuous theories. Examples of complete continuous theories that have this property include Hilbert spaces and any completion of the theory of probability algebras. We also study a weaker notion, the SB-property up (...) to perturbations. This property holds if any two elementarily bi-embeddable models are isomorphic up to perturbations. We prove that the theory of Hilbert spaces expanded with a bounded self-adjoint operator has the SB-property up to perturbations of the operator and that the theory of atomless probability algebras with a generic automorphism have the SB-property up to perturbations of the automorphism. We also study how the SB-property behaves with respect to randomizations. Finally we prove, in the continuous setting, that if T is a strictly stable theory then T does not have the SB-property. (shrink)

A Souslin algebra is a complete Boolean algebra whose main features are ruled by a tight combination of an antichain condition with an infinite distributive law. The present article divides into two parts. In the first part a representation theory for the complete and atomless subalgebras of Souslin algebras is established (building on ideas of Jech and Jensen). With this we obtain some basic results on the possible types of subalgebras and their interrelation. The second part begins with a review (...) of some generalizations of results from descriptive set theory concerning Baire category which are then used in non-trivial Souslin tree constructions that yield Souslin algebras with a remarkable subalgebra structure. In particular, we use this method to prove that under the diamond principle there is a bi-embeddable though not isomorphic pair of homogeneous Souslin algebras. (shrink)

We define a quasi-order on Borel functions from a zero-dimensional Polish space into another that both refines the order induced by the Baire hierarchy of functions and generalises the embeddability order on Borel sets. We study the properties of this quasi-order on continuous functions, and we prove that the closed subsets of a zero-dimensional Polish space are well-quasi-ordered by bi-continuous embeddability.

In lieu of an abstract, here is a brief excerpt of the content:One to NGirard's Philosophy of InnovationJohnathan Bi (bio)What does a theorist of imitation have to teach us about innovation? What could a thinker focused on the distant past have to offer us in building the immediate future? The answer to both questions, I hope to show, is a significant amount. I aim to rescue and develop a neglected strand of Girardian thought from one of his overlooked essays on (...) a topic seemingly antithetical to imitation: innovation. This task proceeds in five steps. First, I articulate two contemporary perspectives on innovation, one dominant and one in the minority. Second, I reconstruct Girard's historical argument from "Innovation and Repetition" in favor of the minority view and, third, his psychological argument against the dominant view. Fourth, I show how Girard's philosophy of innovation sublates crucial features of both poles and provides an alternative mode for conceiving the future.1 Lastly, I wrestle with an immanent objection that threatens the prescriptive force of his entire argument and, even when reconciled, leads me to depart from Girard's conclusions, albeit in the most Girardian of ways. [End Page 71]INNOVATION AND IMITATIONThe dominant view of innovation is that it is opposed to imitation. The foundational type of opposition between the two is metaphysical: imitation and innovation are actions different in kind and must be conceived of as such. Peter Thiel's famous formulation is representative: certain actions, companies, and countries are innovative, going from "zero to one," while others are imitative, going from "one to N."2 This distinction is mostly accepted without question in the social sciences, underpinning entire disciplines such as innovation studies.3 This near-universal consensus, however, is a modern phenomenon. The Latin innovatio, for example, described innovation as being inseparable from the imitation of the past: the Jews returning to Jerusalem, Job having his wealth restored, or the rebirth of a phoenix.4 The word itself reveals as much. Innovatio is derived by appending the prefix in- (within, from inside) to novitas (novelty). It meant novelty that preceded from within, or renewal. Under this view, innovation was not about breaking free or starting from a blank slate, zero to one, but rather rescuing and developing an already formed foundation, one to N. Innovation was identical with the imitation and adaptation of that which is essential but has been obscured. Only beginning in the twentieth century has imitation been so strongly demarcated from innovation.5Built on top of this metaphysical opposition is a practical opposition. Not only are the two actions distinct, they are incompatible: the more one imitates, the more one risks eroding one's ability to innovate. This stronger form of opposition is exemplified by the idea of the "untutored genius" whose source of creativity is solely internal: a fully formed natural endowment not requiring learning nor external inspiration from divinity or nature. This idea gained ascendancy in the seventeenth and eighteenth centuries, and proponents believed that imitation of tradition impeded the expression of one's own innate genius.6 If one wants to write a great book, this idea goes, one ought not read great books for fear that they will crowd out one's original ideas. Even in the twentieth century, Wittgenstein expressed this exact sentiment when he proudly claimed not to have read any Aristotle or engaged deeply with the history of philosophy and considered those who have "academic and therefore unauthentic philosophers."7 Of course, not all modern thinkers see innovation and imitation as practically opposed in such a strong way.8 But even for most who treat the two as harmonious, imitation tends to be relegated to a secondary afterthought as the mere mechanism by which innovation, the primary source of value creation, spreads. This, then, is the third form of opposition drawn out [End Page 72] between the two concepts: a normative one. Imitation is, at best, of secondary value when compared to acts of innovation.The practical and, to a lesser degree, normative oppositions appear so unsound as to not warrant serious engagement, and already contested by theorists who study innovation as to not require another rebuttal. What makes Girard's response to them... (shrink)

Resumen: Este artículo sostiene que algunas Meta-Picto-Poesías del Paisaje compuestas por el poeta estadounidense Gary Snyder toman como tema la pintura china del paisaje con las características de la antigua poesía china, resplandeciente de incomparable encanto artístico y sustancia cultural. La poesía de este tipo es una combinación perfecta de elementos orientales y occidentales, que integra las culturas, los pensamientos y las artes de ambas partes, cuya apreciación crea una experiencia compleja con un híbrido de formas artísticas y espacios estéticos. (...) Gary Snyder no es sólo un eco-poeta, sino también un estilista y un hombre de práctica. Sus obras poéticas revelan la relación de fomento entre literatura, cultura y naturaleza. El artículo pretende hacer un intento transcultural, interdisciplinar y multidisciplinar en la crítica de Snyder, con métodos analíticos que incluyen culturas orientales y occidentales, visiones antiguas y actuales, así como experiencias dinámicas y estáticas. (shrink)

Bilişsel Din Bilimi (CSR), dini inanç ve uygulamaların nedensel açıklamalarını sağlamayı amaçlayan din araştırmalarına bilimsel bir yaklaşımdır. CSR savunucuları, insan zihninin doğal özelliklerini ve nasıl işlediğini açıklayarak dini inançların oluşumu, kabulü, aktarımı ve yaygınlığı sürecini açıklamaya çalışırlar. Tüm insan kültürlerinde var olan ve son on yılda birçok CSR akademisyeninin dikkatini çeken dini inançlardan biri de öbür dünyaya olan inançtır. CSR araştırmacılarına göre, bu inanç, insan zihninin doğal yapılarına dayanmaktadır. Ölümden sonraki hayata olan inancı, zihinsel araçların işleyişinden kaynaklanan, yansıtıcı olmayan veya (...) sezgisel bir inanç olarak görürler. Ölümden sonra hayata inancın oluşumunu, gelişimini, yayılmasını ve aktarılmasını açıklamak için çeşitli teoriler önerdiler. Ancak bu teoriler arasında, iki teori daha geniş kabul görmüştür, sezgisel düalizm teorisi ve simülasyon kısıtlama teorisi. Sezgisel düalizm teorisi, tüm insanların iki zihinsel araca sahip olduğunu söyler: Sezgisel Biyoloji ve Sezgisel Psikoloji. Sezgisel Biyoloji, ölü bir kişinin karşısına geçip hareket edemediği için artık hayatta olmadığına inanmamızı sağlar. Sezgisel Psikoloji, ölü kişiye otomatik olarak görünmez özellikleri (arzular, düşünceler, inançlar ve duygular gibi) atfetmeye devam eder. Yukarıdaki iki zihinsel aracın aynı anda işleyişi, insan zihnini ölü kişinin bir kısmının önemsiz olduğuna ve fiziksel ölümden sonra kaldığına inandırır. Simülasyon kısıtlama teorisi, tüm insanların çevreden gelen bilgileri işlemek ve dini inançlar edinmek için zihinsel araçlara sahip olduğunu söyler. Zihinsel araçların hiçbiri, kişinin arzularının, düşüncelerinin, inançlarının ve duygularının var olmadığını hayal edemez veya simüle edemez. Bu nedenle ölü kişinin karşısındaki insan zihni, fiziksel ölümünü kolayca hayal etmesine rağmen, kişinin başka bir bölümünün (düşünceler, arzular vb.) Varlığına inanmaya devam eder. Bu teorilerin her ikisi de, öbür dünyaya inancın oluşumunu açıklamada zorluklar ve sınırlamalarla karşı karşıya görünüyor. Bunlar arasında nedensel açıklama yapamama, ölümden sonraki hayata olan inancın doğal ve rasyonel temelleri arasındaki ayrım eksikliği ve öbür dünya inancının doğaüstü temellerini göz ardı etme yer alır. İki teoriden hiçbiri öbür dünyaya inancın oluşumu için yeterli nedensel açıklama sağlamıyor gibi görünmektedir. Her iki teori de zihinsel araçların nasıl işlediğine bağlı olarak öbür dünya inançlarının oluşumu hakkında olası bir hikaye sunmaya çalışır. Ölümden sonraki hayata inanmaya yol açan sürecin yalnızca makul bir hikayesini sunarlar. Bu iki teorinin sunduğu şey, insan zihninin ve araçlarının ve bunların nasıl işlediğinin bir açıklamasıdır (nedensel açıklama değil). Bu, kendi başına, bu aletlerin öbür dünyaya bir inanç ürettiğini açıklamaz. Dolayısıyla ahirete olan inancın zihinsel araçların işleyişinin bir sonucu olduğu iddiası, zihinsel araçlar ile bu inanç arasında nedensel bir ilişki gerektirir. Bu iki teoriden hiçbiri bu nedensel ilişkiyi açıklayamaz ve yalnızca aralarındaki ilişkinin makul bir hikayesini açıklarlar. Dahası, dini inancın rasyonel temelleri ile dini inancın doğal temelleri arasındaki ayrım, ahirete inanmak veya onunla ilişkili bilişsel mekanizmaları tanımlamak için doğal bir köken bulmanın hiçbir şekilde bu inancı reddetmek veya itibarını sarsmak anlamına gelmediğini göstermektedir. Ahirete olan inancın doğal kökenleri hakkındaki bilişsel teoriler bize bu inancın rasyonel mi irrasyonel mi olduğunu gösteremez. Bu açıklamalar ancak (eğer yapabilirlerse) bize bu inancın oluşumunun ve yaygınlığının doğal köklerini gösterebilir. Ayrıca Dinsel inanç karmaşık bir kavramdır. Birincisi, doğal bir kavramdır, bu anlamda insan doğasına dayanır ve insanın bilişsel sistemleri ve zihinsel araçlarıyla ilgilidir. İkincisi, kültürel ve sosyal bir kavramdır, bu anlamda hem kültürel ve sosyal değişimden etkilenir hem de onu etkiler. Üçüncüsü, doğaüstü bir kavramdır, bu anlamda hem vahiy hem de kehanet ve insanın maddi olmayan yönüyle derinden bağlantılıdır. Öbür dünyaya inanç, her üç düzeyde açıklamayı gerektiriyor gibi görünüyor. (shrink)

This article discusses Abū ʽUthmān al-Jāḥiẓ (d. 255/869) (one of the first Muʽtazilī scholars) Allah-world relationship, his understanding of custom, and his view on miracles. The Muʻtazilī thinkers examined the problem of miracles within their concept of prophethood. They divide miracles, which they accept as the only proof of prophethood, into two: those under the power of Allah and under the power of the created. Jāḥiẓ explains these two sorts of miracles with the order in the universe established by Allah (...) and people and expresses this order with the concept of custom (ʻāda). Jāḥiẓ divides custom into three. The first of these is the “qā’im (constant) custom”, which is based on the theory of kumūn-ẓuhūr and expresses the general rules that occur as a requirement of the general functioning in the universe. According to Jāḥiẓ “qā’im (constant) custom” is that knowledgeable people are aware of the custom of the universe. This custom is an order created by Allah in the eyes of intelligent and knowledgeable people, which is continuous and therefore cannot be interrupted, and in which there is no chaos. He states that this order is realized through the natures in the objects, which are knowable to everyone. But rarely a nature in this order can be interrupted due to a situation that takes it out of the natural flow and cannot be explained by natural causes. According to him, this is proof that nature, which has the defining feature of the object, is created by the creator, and maintains its continuity based on an arranged program. However, the creator can involve in this order when necessary. In this type of custom, God’s intervention occurs by breaking the qā’im custom that continues on a regular basis. The second of these is the “regional custom”, which is not known to everyone but only known to people living in a certain area. Jāḥiẓ states that the miracle in this type of custom occurred when Allah broke the custom known to the people in the region. The third of these is “social custom” which is established by people. For Jāḥiẓ, the miracles of this kind are under the power of people. He argues that the miracle in this type of custom occurs with sarfa, that is, by God’s intervention with human’s motive or knowledge. In this study, Jāḥiẓ’s view of miracles is discussed together with his theory of nature, his understanding of custom and sarfa. (shrink)

v. 1. al-Nuṣūṣ al-manṭiqīyah -- v. 2. al-Shurūḥ al-manṭiqīyah -- al-mujallad 3. al-Shurūḥ ʻalá al-nuṣūṣ al-manṭiqīyah.

v. 1. Arabic text -- v. 2. English translation.

This study explored the relations between the social support network of mothers of children with autism spectrum disorder, perceived social support, and their subjective wellbeing. The participants were mothers of children with ASD in Shanghai. Their social support network structure was explored via the nomination method. Perceived social support was measured using the Revised Social Provisions Scale for Autism, and the mothers’ subjective wellbeing was assessed using the Index of Wellbeing, Index of General Affect. A significant correlation was observed between (...) the subjective wellbeing of mothers of children with ASD and perceived social support. Meanwhile, perceived social support was significantly correlated with the effectiveness of overall social support. Finally, perceived social support was also significantly correlated with the network size of social support. Moreover, the effectiveness of social support was significantly associated with the network size of social support and was highly significantly associated with the degree of intimacy of social support. Furthermore, the network size of instrumental support has a significant influence on all perceived social support subdimensions. Overall, social support effectiveness plays an important role in the social support network mechanism on perceived social support and subjective wellbeing in China. (shrink)

Prior studies have extensively explored factors that drive misselling behavior in life insurance markets, but considered little the influences of attributes of clients (particularly vulnerable clients) on unethical sales. Our study that is based on the neoclassical theory of the firm aims to investigate the relationships between attributes of life insurance clients and unethical selling behavior of salespeople. Applying logit and probit models to a sample of 35,075 observations from a Chinese life insurance company, our study finds that salespeople are (...) more likely to perform unethical selling to ill-educated clients. Further, when salespeople’s sex and education are considered, the result shows that male or poorly-educated salespeople are more likely to make unethical selling. These findings enrich the literature of misselling of life insurance and offer some practical implications for both insurers and regulators to manage life insurance markets and control misselling behaviors. (shrink)

The Yoga Sutras of Patañjali is the foundational text of yoga philosophy, used by millions of yoga practitioners and students worldwide. This book is a new rendering into English of the Arabic translation and commentary of this text by the brilliant eleventh-century polymath al-Bīrūnī.

تتميز هذه الدراسة عن صوفية الغزالي. رحمة الله. بأنها حققت النظرة المعرفية التي يتبناها، ومناهج البحث التي تسندها وتبعاً لهذا فإنها وفقت في ملاحقة واستنباط معالجة العديد من القضايا التي حفل بها فكره، وهي متشعبة ونجحت في وضعها في مكانها المناسب من البنية المنطقية والمنهجية في فكره. فأثبتت، من غير شك.بأن خطاب الغزالي متماسك الرؤى متلاحم الأجزاء، على عكس ما أشيع عنه الأمر الذي خفف حدة الإشكالية التي اصطبغ بها وساعد، وبالتالي، على تخليصه مما ألحق به من أوهام أو الصق (...) به من مثالب. وفضلا على هذا فقد لفتت الدراسة الانتظار إلى أهمية ( سياسة العلم) التي أخذ بها الغزالي وصمم على أساس منه خطابه، وبينت دورها الخطير في تشكله. كما أنها حللت مفهوم (النور) عنده وهو مفهوم مركزي في خطابه. حيث بينت أنه لا يخرج عن العقلانية بحال. وكذلك تحققت من ركون الغزالي إلى الظاهر البرهاني والتزامه به. قبل أن يتجاوزه في محاولة الارتياد وتأسيس عقلانية أرحب وأرقى كان الغزالي رحمه الله يتطلع إليها وبهذا فقد جاءت هذه الدراسة جديدة حقاً على مستوى الدراسات التي عالجت فكر عالجت فكر الغزالي. واستطاعت أن تغير مفاهيم عدة أشاعتها تلك الدراسات. وبينت تهافت بعض الآراء التي تضمنتها، الأمر الذي يوضح ما قام به الباحث. وإذا نضع بين يديك عزيزنا القارئ هذه الدراسة، فإننا نسأل الله عز وجل أن يوفق الباحث في إعداد دراسات أخرى تنحو ذات المنحى، فتستخرج البنى المعرفية والمنهجية لمفكرين آخرين متميزين في تراثنا العظيم، لتعميق وعينا به، وتدبر آفاقه والله نسأل التوفيق والسداد. (shrink)