We prove that the additive group of the rationals does not have an automatic presentation. The proof also applies to certain other abelian groups, for example, torsion-free groups that are p-divisible for infinitely many primes p, or groups of the form ⊕ p∈I Z(p ∞ ), where I is an infinite set of primes.

Reactive oxygen species (ROS) are known as toxic metabolic products in plants and other aerobic organisms. An elaborate and highly redundant plant ROS network, composed of antioxidant enzymes, antioxidants and ROS-producing enzymes, is responsible for maintaining ROS levels under tight control. This allows ROS to serve as signaling molecules that coordinate an astonishing range of diverse plant processes. The specificity of the biological response to ROS depends on the chemical identity of ROS, intensity of the signal, sites of production, plant (...) developmental stage, previous stresses encountered and interactions with other signaling molecules such as nitric oxide, lipid messengers and plant hormones. Although many components of the ROS signaling network have recently been identified, the challenge remains to understand how ROS-derived signals are integrated to eventually regulate such biological processes as plant growth, development, stress adaptation and programmed cell death. (shrink)

We study the complexity of isomorphism of classes of metric structures using methods from infinitary continuous logic. For Borel classes of locally compact structures, we prove that if the equivalence relation of isomorphism is potentially $\mathbf {\Sigma }^0_2$, then it is essentially countable. We also provide an equivalent model-theoretic condition that is easy to check in practice. This theorem is a common generalization of a result of Hjorth about pseudo-connected metric spaces and a result of Hjorth–Kechris about discrete structures. As (...) a different application, we also give a new proof of Kechris’s theorem that orbit equivalence relations of actions of Polish locally compact groups are essentially countable. (shrink)

Deliberative democrats responding to the challenge of fostering reciprocity and civic friendship discourage in-group deliberations, taking them to stoke hostilities and preclude the possibility of sociability between groups. In opposition to these views, I argue that in-group deliberation presents itself as a promising, yet underappreciated, normative category for conflict transformation. I support this claim with reference to the observation that deliberative exchanges among like members are just as, if not more, consequential in the facilitation of positive actor transformations than deliberations (...) among unlike members, especially when antipathy defines group relations. (shrink)

t. 2. Choveshkata spet︠s︡ifika -- t. 3. Choveshkata pamet.

A notable feature of nationalism's contemporary resurgence is the increasing eagerness of governments to support and shape the political causes of populations living abroad that are viewed as ethnic kindred. However, global criteria for judging when such kin state activism is and is not acceptable have so far remained elusive, as the objectionable instances of the practice tend to overshadow the legally and morally consistent ones. I argue that the analysis of world affairs and promotion of global justice would benefit (...) from an ethic of transnational conduct that has a rightful place for kin states. I defend a set of cosmopolitan criteria for this purpose, outlining how they enable us to recognize and combat the dangers posed by certain forms of kin state mobilization without forgoing the opportunities presented by certain other forms to overcome minority repression and enhance regional security. (shrink)

In this paper an algebraic system of the new type is proposed (namely, a vectorial lattice). This algebraic system is a lattice for the language of Aristotle’s syllogistic and as well as a lattice for the language of Vasiľév’s syllogistic. A lattice for the language of Aristotle’s syllogistic is called a vectorial lattice on cap-semilattice and a lattice for the language of Vasiľév’s syllogistic is called a vectorial lattice on closure cap-semilattice. These constructions are introduced for the first time.

We generalize the notion of analytic/Borel equivalence relations, orbit equivalence relations, and Borel reductions between them to their continuous and quantitative counterparts: analytic/Borel pseudometrics, orbit pseudometrics, and Borel reductions between them. We motivate these concepts on examples and we set some basic general theory. We illustrate the new notion of reduction by showing that the Gromov–Hausdorff distance maintains the same complexity if it is defined on the class of all Polish metric spaces, spaces bounded from below, from above, and from (...) both below and above. Then we show that [Formula: see text] is not reducible to equivalences induced by orbit pseudometrics, generalizing the seminal result of Kechris and Louveau. We answer in negative a question of Ben Yaacov, Doucha, Nies, and Tsankov on whether balls in the Gromov–Hausdorff and Kadets distances are Borel. In appendix, we provide new methods using games showing that the distance-zero classes in certain pseudometrics are Borel, extending the results of Ben Yaacov, Doucha, Nies, and Tsankov. There is a complementary paper of the authors where reductions between the most common pseudometrics from functional analysis and metric geometry are provided. (shrink)

We give a formalism for approximate isomorphism in continuous logic simultaneously generalizing those of two papers by Ben Yaacov [2] and by Ben Yaacov, Doucha, Nies, and Tsankov [6], which are largely incompatible. With this we explicitly exhibit Scott sentences for the perturbation systems of the former paper, such as the Banach‐Mazur distance and the Lipschitz distance between metric spaces. Our formalism is simultaneously characterized syntactically by a mild generalization of perturbation systems and semantically by certain elementary classes of (...) two‐sorted structures that witness approximate isomorphism. As an application, we show that the theory of any ‐tree or ultrametric space of finite radius is stable, improving a result of Carlisle and Henson [8]. (shrink)

In an essential way I make use of Frege’s and Vasilev’s ideas. N. A. Vasilev distinguished two levels in a logic. The abstract logic depends on gnoeologic assumptions while the empirical part of logic depends on ontological ones. Vasilev did not change the external logic but he did change the internal one. His system can be viewed as a non-standard syllogistics based on classical propositional logic . Vasilev’s ideas become plain if we discern cleary acts of (...) predication and acts of assertion, the relation of mental contents with the way things are. The second sourse of the idea seems to Frege’s differentation of mental process and assertion, statement . As a symbol of assertion for Frege serves a vertical stroke |. A horizontal stroke following it is correlated with holding a proposition, it makes the sign determined everywhere. In the string of signs the one following the vertical stroke does not express a proposition, it describes a possible state of affairs. (shrink)

This is the collection of essays presented to Bochenski on his 60th birthday, and it contains, as a mirror of Bochenski's own work, a broad spectrum of studies ranging from formal logic and history of logic, to the philosophy of logic and language, and to the methodology of explanation in Greek philosophy. Of the seventeen articles, these are some of the more important to the reviewer: "Betrachtungen zum Sequenzen Kalkül" by Paul Bernays, which is an extensive study of Gentzen-type formulations (...) of logic; "Remarks on Formal Deduction," H. B. Curry, a further discussion of sequenzen-logics; "Marginalia on Gentzen's Sequenzen Kalkül" by Hughes Leblanc; "Method and Logic in Presocratic Explanation," Jerry Stannard; "On the Logic of Preference and Choice," H. S. Houthakker, a suggestive presentation of decision and utility theory in logical form; "Leibniz's Law in Belief Contexts," Chisholm; "On Ontology and the Province of Logic," R. M. Martin; and "N. A. Vasilev and the Development of Many-valued Logics," G. L. Kline, an important addition to the history of logic. Other contributors are: Storrs McCall, Albert Menne, E. W. Beth, Benson Mates, Ivo Thomas, J. F. Staal, F. R. Barbò, A.-T. Tymieniecka, and N. M. Luyten. There is a bibliography of Bochenski's writings through 1962.—P. J. M. (shrink)