Our purpose in this note is to study countable $\aleph_0$-categorical structures whose theories are tree-decomposable in the sense of Baldwin and Shelah. The permutation group corresponding to such a structure can be decomposed in a canonical manner into simpler permutation groups in the same class. As an application of the analysis we show that these structures are finitely homogeneous.

Sacks [2] has asked whether there exists a uniform solution to Post's problem, i.e. an enumeration operation W such that $\mathbf{d} for every degree d. It is shown here that if such an operation W exists it cannot itself in a particular technical sense be uniform. In fact, the jump operation is characterized amongst such uniform enumeration operations by the condition: $\mathbf{d} for all d. In addition, it is proved that the only other uniform enumeration operations such that d ≤ (...) W (d) for all d are those which equal the identity operation above some fixed degrees. (shrink)

In this note is proved the following:Theorem.Iƒ A × B is universal and one oƒ A, B is r.e. then one of A, B is universal.Letα, τbe 1-argument recursive functions such thatxgoes to, τ) is a map of the natural numbers onto all ordered pairs of natural numbers. A set A of natural numbers is calleduniversalif every r.e. set is reducible to A; A × B is calleduniversalif the set.

Let T be a complete first-order theory over a finite relational language which is axiomatized by universal and existential sentences. It is shown that T is almost trivial in the sense that the universe of any model of T can be written $F \overset{\cdot}{\cup} I_1 \overset{\cdot}{\cup} I_2 \overset{\cdot}{\cup} \cdots \overset{\cdot}{\cup} I_n$ , where F is finite and I 1 , I 2 ,...,I n are mutually indiscernible over F. Some results about complete theories with ∃∀-axioms over a finite relational language (...) are also mentioned. (shrink)

LetT be a universal theory of graphs such that Mod(T) is closed under disjoint unions. Letℳ T be a disjoint union ℳ i such that eachℳ i is a finite model ofT and every finite isomorphism type in Mod(T) is represented in{ℳ i ∶i<Ω3}. We investigate under what conditions onT, Th(ℳ T ) is a coinductive theory, where a theory is called coinductive if it can be axiomatizated by ∃∀-sentences. We also characterize coinductive graphs which have quantifier-free rank 1.

Our purpose in this note is to study countable ℵ0-categorical structures whose theories are tree-decomposable in the sense of Baldwin and Shelah. The permutation group corresponding to such a structure can be decomposed in a canonical manner into simpler permutation groups in the same class. As an application of the analysis we show that these structures are finitely homogeneous.

In this commentary I respond to the claims of Dimitris Vardoulakis that, following a mistake of Heidegger in his translation of Aristotle and the apparent loss of phronêsis, post-war continental philosophy has abandoned instrumental rationality and the calculation of utility, instead valorizing an ‘action without ends’ and instituting a ‘new Kantianism’ in its ethics, politics, and ontology. I do so by presenting the thought of Gilles Deleuze as one identified in this tradition who fails to be characterized by Vardoulakis’s claims, (...) and whose concepts already address these concerns. I first demonstrate how Deleuze’s ontology, as presented in Difference and Repetition, avoids relying on or constructing a meaningful, ontological outside, and so Vardoulakis’s characterization of a new Kantianism. And secondly, I respond to Vardoulakis’s critique of continental ethics by presenting the ethical notions in both The Logic of Sense and Capitalism and Schizophrenia as stemming from distinct ethical heritages (the former building on that of the Stoics, the latter primarily that of Spinoza), as well as both providing immanent direction to our actions, providing what can be read as the revisable, calculable reasoning Vardoulakis associates with phronêsis. In this way I show that his category of the ‘ineffectual’ cannot apply to all post-war continental philosophy as Vardoulakis so claims. (shrink)

Virtually every figure in the climate justice literature agrees that states are presently failing to discharge their duties to take action on climate change. Few, however, have attempted to think through what follows from that fact from a moral point of view. In Climate Justice Beyond the State, Lachlan Umbers and Jeremy Moss argue that states’ failures to take action on climate change have important implications for the duties of the most important actors states contain within them – sub-national (...) political communities, corporations, and individuals – actors that have been largely neglected in the climate justice literature, to date. Sub-national political communities and corporations, they argue, have duties to immediately, aggressively, and unilaterally reduce their emissions. Individuals, on the other hand, have duties to help promote collective action on climate change. Along the way, they contribute to a range of important contemporary debates, including those over the nature of collective duties, what agents are required to do under conditions of partial compliance, and the requirements of fairness. Targeted at academic philosophers working on climate justice, this book will also be of great interest to students and scholars of global justice, applied ethics, political philosophy, and environmental humanities. (shrink)

Dissatisfaction with democratic institutions has run high in recent years. Perhaps as a result, political theorists have begun to turn their attention to possible alternative modes of political dec...