On a Glimm -- Effros dichotomy theorem for Souslin relations in generic universes

We prove that if every real belongs to a set generic extension of the constructible universe then every \Sigma_1^1 equivalence E on reals either admits a Delta_1^HC reduction to the equality on the set 2^{<\om_1} of all countable binary sequences, or continuously embeds E_0, the Vitali equivalence. The proofs are based on a topology generated by OD sets

The Universality Problem

The theme of this thesis is to explore the universality problem in set theory in connection to model theory, to present some methods for finding universality results, to analyse how these methods were applied, to mention some results and to emphasise some philosophical interrogations that these aspects entail. A fundamental aspect of the universality problem is to find what determines the existence of universal objects. That means that we have to take into consideration and examine the methods that we use in proving their existence or nonexistence, the role of cardinal arithmetic, combinatorics etc. The proof methods used in the mathematical part will be mostly set-theoretic, but some methods from model theory and category theory will also be present. A graph might be the simplest, but it is also one of the most useful notions in mathematics. We show that there is a faithful functor F from the category L of linear orders to the category G of graphs that preserves model theoretic-related universality results (classes of objects having universal models in exactly the same cardinals, and also having the same universality spectrum). Trees constitute combinatorial objects and have a central role in set theory. The universality of trees is connected to the universality of linear orders, but it also seems to present more challenges, which we survey and present some results. We show that there is no embedding between an ℵ2-Souslin tree and a non-special wide ℵ2 tree T with no cofinal branches. Furthermore, using the notion of ascent path, we prove that the class of non-special ℵ2-Souslin tree with an ω-ascent path a has maximal complexity number, 2ℵ2 = ℵ3. Within the general framework of the universality problem in set theory and model theory, while emphasising their approaches and their connections with regard to this topic, we examine the possibility of drawing some philosophical conclusions connected to, among others, the notions of mathematical knowledge, mathematical object and proof

Cosmological Applications of Extended Theories of Gravity

This work investigates the cosmological applications of higher-order theories of gravity in four dimensions. In particular, we begin dealing with the possibility to obtain massive modes in the framework of effective field theories recovered by extending General Relativity and taking into account generic functions of the curvature invariants. In particular, adopting the minimal extension of f(R) gravity, an effective field theory with massive modes is straightforwardly recovered. This approach allows to evade shortcomings like ghosts and discontinuities if a suitable choice of expansion parameters is performed. Next, we stress one of the most important problem related to Extended Theories of Gravity that is the lack of a definitive, unique theory able to address the different shortcomings of General Relativity. In fact, several models have been proposed in order to address the dark side problem in cosmology and these models should be constrained also at ultraviolet scales in order to achieve a correct fundamental interpretation. We proceed analyzing the possibility to constrain f(R) theories at UV scales comparing quantum vacuum states in given cosmological back- grounds. Specifically, we compare Bogolubov transformations associated to different vacuum states for some f(R) models. The procedure consists in fixing the f(R) free parameters by requiring that the Bogolubov coefficients can be correspondingly mini- mized to be in agreement with both high redshift observations and quantum field theory predictions. In such a way, the particle production is related to the value of the Hubble parameter and then to the given f (R) model. The approach is developed in both metric and Palatini formalism. The second part of this thesis is devoted to the search for exact solutions for Ex- tended Theories of Gravity that is very useful in order to control the physical meaning of these theories. To this goal, useful tools are Noether and Hojman approaches. The application of Hojman conservation theorem is presented in the framework of scalar-tensor cosmologies allowing to fix the form of the coupling F (φ), of the potential V (φ) and to find out exact solutions for related cosmological models. Afterwards, Noether point symmetries are applied to metric-Palatini hybrid gravity in order to select the f(R) functional form, to find analytical solutions for the field equations and for the related Wheeler-DeWitt equation and finally to Gauss-Bonnet cosmological models, where F is a generic function of the curvature scalar R and the Gauss-Bonnet topological invariant G, showing that the functional form of the F(R,G) function can be determined by the presence of symmetries. Exact solutions for some specific cosmological models are found out. Finally, cosmological inflation is discussed in the framework of F(R,G) gravity. In principle, this theory can exhaust all the curvature budget related to curvature invariants. Cosmological dynamics is analysed resulting driven by two effective scalar fields, specifically a R scalaron and a G scalaron, working respectively at early and very early epochs of cosmic evolution. In this sense, a double inflationary scenario naturally emerges

Back to the Future. The Future in the Past. Conference Proceedings Book

ICDHS is the acronym of the International Committee of De­sign History and Design Studies, an organisation that brings together scholars from Spain, Cuba, Turkey, Mexico, Finland, Japan, Belgium, the Netherlands, Brazil, Portugal, the US, Tai­wan, Canada and the UK. Since 1999, when the Design and Art History departments of the University of Barcelona organised the first edition of the ICDHS, a conference has been held every two years at a different venue around the world. These conferences have had two dis­tinct aims: first, to present original research in the fields of Design History and Design Studies and, second, to include contributions in these fields from non-hegemonic countries, offering a speaking platform to many scientific communities that are already active or are forming and developing. For that reason, the structure of the conferences combines many paral­lel strands, including poster presentations and keynote speak­ers who lecture on the conferences’ main themes. The 2018 event is rather special. The Taipei 2016 conference was the 10th edition and a commemoration of the ten celebrations to date. Returning to Barcelona in 2018 marks the end of one stage and the beginning of a new one for the Committee. The numbering chosen—“10+1”—also means that Barcelona 2018 is both an end and a beginning in the ICDHS’s own history. The book brings together 137 papers delivered at the ICDHS 10th+1 Conference held in Barcelona on 29–31 October 2018. The papers are preceded by texts of the four keynote lectures and a written tribute from the ICDHS Board to its founder and figurehead, Anna Calvera (1954–2018). The Conference, and the book, are dedicated to her memory

Back to the future. The future in the past: ICDHS 10th+1 Barcelona 2018: Conference proceedings book

Obra dedicada a la memòria d'Anna Calvera (1954–2018).Conté: 0. Opening pages -- 1.1 Territories in the scene of globalised design: localisms and cosmopolitanisms -- 1.2 Designing the histories of southern designs -- 1.3 Mediterranean-ness: an inquiry into design and design history -- 1.4 From ideology to methodology: design histories and current developments in post-socialist countries -- 1.5 [100th anniversary of the Bauhaus Foundation]: tracing the map of the diaspora of its students -- 1.6 Design history: gatekeeper of the past and passport to a meaningful future? -- 1.7 Constructivism and deconstructivism: global development and criticism -- 1.8 An expanded global framework for design history -- 1.9 Design museums network: strengthening design by making it part of cultural legacy -- 1.10 Types and histories: past and present issues of type and book design -- 2.1 Design aesthetics: beyond the pragmatic experience and phenomenology -- 2.2 Public policies on design and design-driven innovation -- 2.3 Digital humanities: how does design in today's digital realm respond to what we need? -- 2.4 Design studies: design methods and methodology, the cognitive approach -- 2.5 Vehicles of design criticism -- 3 Open session: research and works in progress (1) -- 3 Open session: research and works in progress (2) -- Addenda: 10th+I keywords mapInternational Committee of Design History and Design Studies. Conference (11a : 2018 : Barcelona, Catalunya),ICDHS is the acronym of the International Committee of De­sign History and Design Studies, an organisation that brings together scholars from Spain, Cuba, Turkey, Mexico, Finland, Japan, Belgium, the Netherlands, Brazil, Portugal, the US, Tai­wan, Canada and the UK. Since 1999, when the Design and Art History departments of the University of Barcelona organised the first edition of the ICDHS, a conference has been held every two years at a different venue around the world. These conferences have had two dis­tinct aims: first, to present original research in the fields of Design History and Design Studies and, second, to include contributions in these fields from non-hegemonic countries, offering a speaking platform to many scientific communities that are already active or are forming and developing. For that reason, the structure of the conferences combines many paral­lel strands, including poster presentations and keynote speak­ers who lecture on the conferences’ main themes. The 2018 event is rather special. The Taipei 2016 conference was the 10th edition and a commemoration of the ten celebrations to date. Returning to Barcelona in 2018 marks the end of one stage and the beginning of a new one for the Committee. The numbering chosen—“10+1”—also means that Barcelona 2018 is both an end and a beginning in the ICDHS’s own history. The book brings together 137 papers delivered at the ICDHS 10th+1 Conference held in Barcelona on 29–31 October 2018. The papers are preceded by texts of the four keynote lectures and a written tribute from the ICDHS Board to its founder and figurehead, Anna Calvera (1954–2018). The Conference, and the book, are dedicated to her memory

Workshop on Squeezed States and Uncertainty Relations

The proceedings from the workshop are presented, and the focus was on the application of squeezed states. There are many who say that the potential for industrial applications is enormous, as the history of the conventional laser suggests. All those who worked so hard to produce squeezed states of light are continuing their efforts to construct more efficient squeezed-state lasers. Quite naturally, they are looking for new experiments using these lasers. The physical basis of squeezed states is the uncertainty relation in Fock space, which is also the basis for the creation and annihilation of particles in quantum field theory. Indeed, squeezed states provide a unique opportunity for field theoreticians to develop a measurement theory for quantum field theory

The impact of mathematics teaching efficacy on teachers’ pedagogical practices

This study explores the pedagogical practices of 167 Year 4 and 160 Year 8 New Zealand mathematics teachers who have different levels of mathematics teaching efficacy. Using data from the National Monitoring Study of Student Achievement 2013, the teacher questionnaire items believed to be the indicators of mathematics teaching efficacy were selected, represented by six items such as “I feel confident about teaching maths”. Then, low, mid, and high efficacious teachers were identified and compared to see how they differed with respect to their teaching profile and the frequency they used effective pedagogies when teaching mathematics (italicised below) (Anthony &amp; Walshaw, 2007). Twenty eight percent of Year 4 and 41% of Year 8 teachers had high mathematics teaching efficacy. Compared with the other teachers, teachers with high mathematics teaching efficacy were better able to provide an ethic of care in their classroom, they more frequently arranged their classrooms for learning to enable students to collaborate, and more frequently expected their students to communicate their thinking and debate ideas with others. They more frequently provided students with worthwhile mathematical tasks, they more frequently provided opportunities for their students to build on their own thinking, and to explore how new learning linked to or changed what they already knew. They more frequently expected their students to make mathematical connections by reflecting on their learning, to use multiple representations, and use ideas and skills from different curriculum areas