§0. Preface. There has been an expectation that the endgame of the more tenacious problems raised by the Los Angeles ‘cabal’ school of descriptive set theory in the 1970's should ultimately be played out with the use of inner model theory. Questions phrased in the language of descriptive set theory, where both the conclusions and the assumptions are couched in terms that only mention simply definable sets of reals, and which have proved resistant to purely descriptive set theoretic arguments, may (...) at last find their solution through the connection between determinacy and large cardinals.Perhaps the most striking example was given by [24], where the core model theory was used to analyze the structure of HOD and then show that all regular cardinals below ΘL are measurable. John Steel's analysis also settled a number of structural questions regarding HODL, such as GCH.Another illustration is provided by [21]. There an application of large cardinals and inner model theory is used to generalize the Harrington-Martin theorem that determinacy implies )determinacy.However, it is harder to find examples of theorems regarding the structure of the projective sets whose only known proof from determinacy assumptions uses the link between determinacy and large cardinals. We may equivalently ask whether there are second order statements of number theory that cannot be proved under PD–the axiom of projective determinacy–without appealing to the large cardinal consequences of the PD, such as the existence of certain kinds of inner models that contain given types of large cardinals. (shrink)

Open peer commentary on the article “Elementary Students’ Construction of Geometric Transformation Reasoning in a Dynamic Animation Environment” by Alan Maloney. Upshot: Parnorkou and Maloney’s article presents an interesting, well-structured and clearly described study of children’s reasoning about mental rotations. Specifically, Parnorkou and Maloney deploy the microworld Graphs ’n Glyphs, and use it as a “window on thinking-in-change” as they observe and interview children who use it. Reading the article raised a few questions for me about the role of body (...) syntonicity in learning about rotation of geometric shapes, and I wonder where the authors feel these foundational concepts fit in with their research. (shrink)

Open peer commentary on the article “Circularity and the Micro-Macro-Difference” by Manfred Füllsack. Upshot: Füllsack provides a convincing argument for viewing circularity through a systems sciences perspective and for seeing micro-level emergence as an explanatory lens for phenomena that are circular at the macro-level. However, as an educator focusing on reasoning about circular macro-level phenomena through explanations at the micro-level, I see a series of issues relating designing appropriate learning experiences and fundamentally defining what this kind of thinking looks like.

Michael Oakeshott’s distinction between ‘civil association’ and ‘enterprise association’ has inspired international society theorists to conceive of international society as not just a ‘purposive association’ constructed by states to satisfy their interests but also as a ‘practical association’ providing formal and pragmatic rules that are not instrumental to particular goals of state policy. While this article is supportive of the Oakeshottian turn in international society theory, it suggests that somewhat different conclusions can be drawn from it. The article sketches out (...) an alternative conception of international ‘civil association’, one that transcends the boundaries of communities. It is argued that such a notion of civil association is both possible and at the same time anchored in the experiences of the modern state. It is suggested that this notion of international civil association, when sustained by an adequate legal conception, promotes the enforcement of moral and political responsibility acr... (shrink)

If some infinitary sentence provides a counterexample to Vaught's Conjecture, then there is an infinitary sentence which also provides a counterexample but has no model of cardinality bigger than ℵ₁.

Comparing the nature encounters of Gerald Durrell with our current climate of ‘stranger danger’, health and safety neurosis, and the beguilement and blunting of the senses by technological advances presents a worrying picture of a new era of nature and culture deprivation. However, even in the most unlikely places, a rich engagement with nature can be rekindled. Central to such recovery is access to nearby nature that allows practical engagement rather than merely detached on-looking. In my conclusion I outline examples (...) where this has been made possible in the challenging settings of socially deprived urban areas. (shrink)

We prove that if p ≠ q are distinct primes, then the classification problems for p-local and q-local torsion-free abelian groups of rank two are incomparable with respect to Borel reducibility.

This paper shows that while there seems to be more or less a general acceptance for plurality as a condition of world politics and at least a vague commitment to a pluralist ideal, the challenge remains to formulate a fruitful account of international pluralism. While dominating approaches to international theory present international pluralism as essentially a by-product and instrumental, this paper suggest an alternative way to conceive of international pluralism when defending the ancient concept variety as a better guide to (...) approach both the understanding of plurality as the human condition and the notion of international pluralism. The paper concludes that it is preferable to accept a variety of pluralist conceptions rather than go on searching for a theoretical conception standing above the controversy; accepting pluralism in a sense involves rejecting just one version of pluralism. (shrink)

If there is a good $\Delta^1_3$ wellordering of the reals, then there is a $\Pi^1_1$ wellfounded relation for which the comparison relation is not projective.

As social, locative, and mobile media render the intimate public and the public intimate, this volume interrogates how this phenomenon impacts art practice and politics. Contributors bring together the worlds of art and media culture to rethink their intersections in light of participatory social media. By focusing upon the Asia-Pacific region, they seek to examine how regionalism and locality affect global circuits of culture. The book also offers a set of theoretical frameworks and methodological paradigms for thinking about contemporary art (...) practice more generally. (shrink)

We show that every dominating analytic set in the Baire space has a dominating closed subset. This improves a theorem of Spinas [15] saying that every dominating analytic set contains the branches of a uniform tree, i.e. a superperfect tree with the property that for every splitnode all the successor splitnodes have the same length. In [15], a subset of the Baire space is called u-regular if either it is not dominating or it contains the branches of a uniform tree, (...) and it was proved that Σ21-Kσ-regularity implies Σ21-u-regularity. Here we show that these properties are in fact equivalent. Since the proof of analytic u-regularity uses a game argument it was clear that determinacy implies u-regularity of all sets. Here we show that an inaccessible cardinal is enough to construct a model for projective u-regularity, namely it holds in Solovay's model. Finally we show that forcing with uniform trees is equivalent to Laver forcing. (shrink)

Using the theory of Borel equivalence relations we analyze the isomorphism relation on the countable models of a theory and develop a framework for measuring the complexity of possible complete invariants for isomorphism.

Assuming AD + DC, we characterize the self-dual boldface pointclasses which are strictly larger than the pointclasses contained in them: these are exactly the clopen sets, the collections of all sets of Wadge rank [Formula: see text], and those of Wadge rank [Formula: see text] when ξ is limit.

We consider Borel equivalence relations E induced by actions of the infinite symmetric group, or equivalently the isomorphism relation on classes of countable models of bounded Scott rank. We relate the descriptive complexity of the equivalence relation to the nature of its complete invariants. A typical theorem is that E is potentially Π03 iff the invariants are countable sets of reals, it is potentially Π04 iff the invariants are countable sets of countable sets of reals, and so on. The proofs (...) use various techniques, including Vaught transforms, changing topologies, and the Scott analysis of countable models. (shrink)

We show that every ℵα can be characterized by the Scott sentence of some countable model; moreover there is a countable structure whose Scott sentence characterizes ℵ1 but whose automorphism group fails the topological Vaught conjecture on analytic sets. We obtain some partial information on Ulm type dichotomy theorems for the automorphism group of Knight's model.

We announce two new dichotomy theorems for Borel equivalence relations, and present the results in context by giving an overview of related recent developments.§1. Introduction. For X a Polish space and E a Borel equivalence relation on X, a classification of X up to E-equivalence consists of finding a set of invariants I and a map c : X → I such that xEy ⇔ c = c. To be of any value we would expect I and c to be (...) “explicit” or “definable”. The theory of Borel equivalence relations investigates the nature of possible invariants and provides a hierarchy of notions of classification.The following partial ordering is fundamental in organizing this study. Given equivalence relations E and F on X and Y, resp., we say that E can be Borel reduced to F, in symbolsif there is a Borel map f : X → Y with xEy ⇔ fFf. Then if is an embedding of X/E into Y/F, which is “Borel”.Intuitively, E ≤BF might be interpreted in any one of the following ways: The classi.cation problem for E is simpler than that of F: any invariants for F work as well for E. One can classify E by using as invariants F-equivalence classes. The quotient space X/E has “Borel cardinality” less than or equal to that of Y/F, in the sense that there is a “Borel” embedding of X/E into Y/F. (shrink)

The picturesque is usually interpreted as an admiration of 'picture-like,' and thus inauthentic, nature. In contrast, this paper sets out an interpretation that is more in accord with the contemporary love of wildness. This paper will briefly cover some garden history in order to contextualize the discussion and proceed by reassessing the picturesque through the eighteenth century works of Price and Watelet. It will then identify six themes in their work (variety, intricacy, engagement, time, chance, and transition) and show that, (...) far from forcing a 'picture-like' stereotype on nature, the picturesque guided the way for a new appreciation of wildness—one that resonates with contemporary environmental philosophy. (shrink)

Comparing the nature encounters of Gerald Durrell with our current climate of ‘stranger danger’, health and safety neurosis, and the beguilement and blunting of the senses by technological advances presents a worrying picture of a new era of nature and culture deprivation. However, even in the most unlikely places, a rich engagement with nature can be rekindled. Central to such recovery is access to nearby nature that allows practical engagement rather than merely detached on-looking. In my conclusion I outline examples (...) where this has been made possible in the challenging settings of socially deprived urban areas. (shrink)

The study of continuous group actions is ubiquitous in mathematics, and perhaps the most general kinds of actions for which we can hope to prove theorems in just ZFC are those where a Polish group acts on a Polish space.For this general class we can find works such as [29] that build on ideas from ergodic theory and examine actions of locally compact groups in both the measure theoretic and topological contexts. On the other hand a text in model theory, (...) such as [12], will typically consider issues bearing on the actions by the symmetric group of all permutations of the integers. More generally [1] shows that the orbit equivalence relations induced by closed subgroups of the infinite symmetric group can be reduced to the isomorphism relation on corresponding classes of countable models.This paper considers a third category formed by the continuous actions of separable Banach spaces on Polish spaces. These examples cannot be subsumed under the two earlier headings, and it is known from [10] that theBorel cardinalitiesof the quotient spaces that arise from such actions are incomparable with the equivalence relations induced by the symmetric group or any locally compact Polish group action.One of the first things to be addressed concerns the complexity of these equivalence relations. This question forappears in [1]. (shrink)

Reference to Merleau-Ponty's ideas surfaces in environmental thinking from time to time. This paper examines whether, and in what way, his ideas could be helpful to that thinking. In order to arrive at a conclusion I examine in detail and attempt to clarify the notions of 'Flesh' and 'Earth' in order to see if they can carry the meanings that commentators sometimes attribute to them. With a clearer outline of what he was saying in place, I suggest that the new (...) ontology that Merleau-Ponty introduces could help to transform environmental thinking, but that careful argumentation is required to show this. (shrink)

Let E be a Σ1 1 equivalence relation for which there does not exist a perfect set of inequivalent reals. If 0# exists or if V is a forcing extension of L, then there is a good ▵1 2 well-ordering of the equivalence classes.

In the presence of large cardinals, or sufficient determinacy, every equivalence relation in L(R) either admits a wellordered separating family or continuously reduces E 0.

The Handbook examines 34 philosophical thinkers, both those commonly linked to process thinking, such as Whitehead, Bergson and James, and those that are not as often addressed from a process perspective such as Dilthey and Tarde. Each chapter addresses the background and context of this thinker, their work, and the potential contribution to organization and management research.

This Handbook presents key ideas of philosophers and social theorists whose ideas inform process approaches to organization studies. Each chapter addresses the background and context of this thinker, their work (with a focus on the processual elements), and the potential contribution to organization and management research.

Literature on place makes use of concepts like authenticity and is often structured around a critique of homogeneity or placelessness. This critique is reinforced by the discourse of conservation biology with its emphasis on protecting biodiversity and condemning some non-native species. However, a common emotional response of humans, when they are displaced, is to make where they are like where they felt at home. The debate around invasive species needs careful handling for both ecological and social reasons. This paper addresses (...) a gap in that debate by taking account of the emotional involvement of humans with plants and their caring for the immediate environment through the activity of gardening. (shrink)

Through a number of examples of environmental interventions, this paper makes the claim that the unauthorised nature of some interventions is an integral part of their aesthetic quality. This does not mean that all such interventions have these qualities - only that the regulation of what can be done where and by whom could endanger the production of a rich seam of aesthetic experience, such as edginess and whimsy, and the aesthetic engagement of artists and the general public with places.

There is an ergodic, measure preserving, countable Borel equivalence relation E on a standard Borel probability space (X, µ) such that E\c is not essentially free on any conull C ⊂ X.

§0. Preface. There has been an expectation that the endgame of the more tenacious problems raised by the Los Angeles ‘cabal’ school of descriptive set theory in the 1970's should ultimately be played out with the use of inner model theory. Questions phrased in the language of descriptive set theory, where both the conclusions and the assumptions are couched in terms that only mention simply definable sets of reals, and which have proved resistant to purely descriptive set theoretic arguments, may (...) at last find their solution through the connection between determinacy and large cardinals.Perhaps the most striking example was given by [24], where the core model theory was used to analyze the structure of HOD and then show that all regular cardinals below ΘL are measurable. John Steel's analysis also settled a number of structural questions regarding HODL, such as GCH.Another illustration is provided by [21]. There an application of large cardinals and inner model theory is used to generalize the Harrington-Martin theorem that determinacy implies )determinacy.However, it is harder to find examples of theorems regarding the structure of the projective sets whose only known proof from determinacy assumptions uses the link between determinacy and large cardinals. We may equivalently ask whether there are second order statements of number theory that cannot be proved under PD–the axiom of projective determinacy–without appealing to the large cardinal consequences of the PD, such as the existence of certain kinds of inner models that contain given types of large cardinals. (shrink)

The Martin-Steel coarse inner model theory is employed in obtaining new results in descriptive set theory. $\underset{\sim}{\Pi}$ determinacy implies that for every thin Σ 1 2 equivalence relation there is a Δ 1 3 real, N, over which every equivalence class is generic--and hence there is a good Δ 1 2 (N ♯ ) wellordering of the equivalence classes. Analogous results are obtained for Π 1 2 and Δ 1 2 quasilinear orderings and $\underset{\sim}{\Pi}^1_2$ determinacy is shown to imply that (...) every Π 1 2 prewellorder has rank less than $\underset{\sim}{\delta}^1_2$. (shrink)