Coarse groups, and the isomorphism problem for oligomorphic groups

Let [Formula: see text] denote the topological group of permutations of the natural numbers. A closed subgroup [Formula: see text] of [Formula: see text] is called oligomorphic if for each [Formula: see text], its natural action on [Formula: see text]-tuples of natural numbers has only finitely many orbits. We study the complexity of the topological isomorphism relation on the oligomorphic subgroups of [Formula: see text] in the setting of Borel reducibility between equivalence relations on Polish spaces. Given a closed subgroup [Formula: see text] of [Formula: see text], the coarse group [Formula: see text] is the structure with domain the cosets of open subgroups of [Formula: see text], and a ternary relation [Formula: see text]. This structure derived from [Formula: see text] was introduced in [A. Kechris, A. Nies and K. Tent, The complexity of topological group isomorphism, J. Symbolic Logic 83(3) (2018) 1190–1203, Sec. 3.3]. If [Formula: see text] has only countably many open subgroups, then [Formula: see text] is a countable structure. Coarse groups form our main tool in studying such closed subgroups of [Formula: see text]. We axiomatize them abstractly as structures with a ternary relation. For the oligomorphic groups, and also the profinite groups, we set up a Stone-type duality between the groups and the corresponding coarse groups. In particular, we can recover an isomorphic copy of [Formula: see text] from its coarse group in a Borel fashion. We use this duality to show that the isomorphism relation for oligomorphic subgroups of [Formula: see text] is Borel reducible to a Borel equivalence relation with all classes countable. We show that the same upper bound applies to the larger class of closed subgroups of [Formula: see text] that are topologically isomorphic to oligomorphic groups.

Eco-translatology-based Analysis of Children’s Literature Translation—A Case Study: Peter Pan

Children’s literature occupies a peripheral position in literature system according to the polysystem theory so that the translators of children’s literature can manipulate the texts with great liberty. The translator of children’s literature in the ternary relation of translation, namely the source texts, the translator and the target text, is in a relatively important position. Thus, it is a feasible way to analyze the translation of children’s literature from the translator-centered perspective. Eco-translatology is a translator-centered translation theory, aiming to analyze how the translator selects and adapts during the translation process in the translational eco-environment. In this paper, the author will adopt Eco-translatology as the translation framework to analyze the translation of children’s literature, and try to explore how ‘children’, an important factor in the translational eco-environment, influences the translator’s selection and adaptation in the process of translating children’s literature. Furthermore, the author will take Peter Pan as a case study, comparing two Chinese versions of this book to analyze how the two translators adapt and select differently from those three dimensions during the translation process, as one follows the target-reader-oriented strategy and the other one follows the source-text-oriented strategy.

Information Flow in Logics in the Vicinity of BB

Situation theory, and channel theory in particular, have been used to provide motivational accounts of the ternary relation semantics of relevant, substructural, and various non-classical logics. Among the constraints imposed by channel-theory, we must posit a certain existence criterion for situations which result from the composites of multiple channels (this is used in modeling information flow). In associative non-classical logics, it is relatively easy to show that a certain such condition is met, but the problem is trickier in non-associative logics. Following Tedder (2017), where it was shown that the conjunction-conditional fragment of the logic B admits the existence of composite channels, I present a generalised ver- sion of the previous argument, appropriate to logics with disjunction, in the neighbourhood ternary relation semantic framework. I close by suggesting that the logic BB+(^I), which falls between Lavers' system BB+ and B+ , satisfies the conditions for the general argument to go through (and prove that it satisfies all but one of those conditions).

Digital Jordan Curves and Surfaces with Respect to a Closure Operator

In this paper, we propose new definitions of digital Jordan curves and digital Jordan surfaces. We start with introducing and studying closure operators on a given set that are associated with n-ary relations (n > 1 an integer) on this set. Discussed are in particular the closure operators associated with certain n-ary relations on the digital line ℤ. Of these relations, we focus on a ternary one equipping the digital plane ℤ2 and the digital space ℤ3 with the closure operator associated with the direct product of two and three, respectively, copies of this ternary relation. The connectedness provided by the closure operator is shown to be suitable for defining digital curves satisfying a digital Jordan curve theorem and digital surfaces satisfying a digital Jordan surface theorem.

Entre parole et histoire

Witnessing is an increasingly important theme in the work of Jean-Luc Marion. According to Marion, the witness can be considered an appropriate figure to define the first person, the “I,” without reducing it to subjectivism and without envisaging the intersubjective tie as binary (dual or dialogic), inasmuch as the testimony refers instead to a ternary relation. The present analysis investigates the difference Marion identifies between the religious witness and what seems to be, according to common sense, the regular witness. While in the latter case, the subject is completely foreign to the event to which s/he testifies, in the case of the religious witness, the commitment is total. We will tackle this difference by showing that the fact of testifying always implies a connection with effectivity, which reveals itself through the profound commitment characterizing the witness’s life, up to the point of death. This becomes obvious when considering the role played by the witness’s confessing speech, which establishes an unsurpassable ternary relationship between the witness, the object of the testimony, and the one to whom it is addressed, by deploying an absolute form of the social bond.

Le redoublement syntaxique des adverbes relatifs-interrogatifs et indéfinis (temps, manière et quantité) par les adverbes d’altérité correspondants en roumain actuel

The Syntactic Doubling of Relative-interrogative and Indefinite (Temporal, Modal and Quantitative Adverbials) through Corresponding Alterity Adverbials in Present-day Romanian. This study represents a continuation of a previous study (Chircu 2020b); it discusses the distribution of (temporal, modal and quantitative) alterity adverbials which syntactically double semantically equivalent relative-interrogative and indefinite adverbials. The alterity adverbials strengthen the meaning of the relative-interrogative and indefinite adverbials and offer alternative solutions of fulfilling the action expressed by the verb or, in the case of modal adverbials, of satisfying the constraints of a ternary relation. In the identified contexts, it can be observed that the alterity adverbial is used both anaphorically and cataphorically, depending of the choice of the speakers. For this analysis, the author has extracted data from the present-day language (the CoRoLa corpus and Google).

A logic of hypothetical conjunction

A binary connective that can be read as a matching conjunction for conditional connectives found in many conditional logics is considered. The most natural way to read this connective is often as a conjunction and yet, hypothetically, considered to hold of a state of affairs that could be obtained under the hypothesis. The connective can be given an intensional semantics extending a standard semantics of conditional logic that uses propositionally indexed families of binary relations on possible worlds. This semantics is determined by an adjoint relationship between the operations supporting the semantics of the conditional and the new conjunction. The semantics of the hypothetical conjunction connective subsumes the semantics, supported by a ternary relation semantics, of the fusion connective that arises in connection with substructural and relevant logics, and therefore subsumes a number of other forms of conjunction. A number of applications of the hypothetical conjunction connective are discussed, including generalized forms of resource reasoning used in computer science applications.

On the Compatibility of a Ternary Relation with a Binary Fuzzy Relation

Recently, De Baets et al. have characterized the fuzzy tolerance relations that a given strict order relation is compatible with. In general, the compatibility of a strict order relation with a binary fuzzy relation guarantees also the compatibility of its associated betweenness relation with that binary fuzzy relation. In this paper, we study the compatibility of an arbitrary ternary relation with a binary fuzzy relation. We prove that this compatibility can be expressed in terms of inclusions of the binary fuzzy relation in the traces of the given ternary relation.