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Consolidated Research Groups (DURSI)
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| Group: | Research Group in Logic (DURSI, 2005SGR-00738) | |
| Renewal: | 2008 | |
| Scientist in charge: | Enrique Casanovas | |
| Topics: | Boolean algebras; model theory: stability and simple theories, model-theoretic algebra, and automorphisms groups; axiomatic set theory: descriptive set theory, forcing, infinitary combinatorics and applications to analysis; foundations of mathematics; philosophy of logic and mathematics. | |
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| Group: | Research Group on Non-classical Logics (DURSI, 2005SGR-00083) | |
| Renewal: | 2008 | |
| Scientist in charge: | Ramon Jansana | |
| Topics: | Modal logic, Intuitionistic logic, Substructural logics, Many-valued logics, Algebraic Logic, Abstract Algebraic Logic. | |
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| Group: | LOGOS. Logic Language and Cognition Research Group. (2005 SGR00734) | |
| Renewal: | 2008 | |
| Coordinator: | Genoveva Martí | |
| Topics: | Theory of reference; relations between semantics and pragmatics; non truth-conditional aspects of meaning; vagueness; relativism; knowledge of meaning; mind and language; conceptual aspects of cognitive neuroscience; the nature of conscious experience; theories of truth; the notion of logical consequence; essence and modality; scientific concepts and scientific models; theories of concepts and the a priori; externalism; epistemic justification. | |
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European Research Projects
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| Project: | Mindreading and the emergence of communication: the case of reference (European Science Foundation, BFF2002-10164-E) | |
| Period: | 2003-2006 | |
| Scientist in charge: | Manuel García-Carpintero | |
| Goals: | The goal of the whole project is contributing to articulate an ontological framework invoking as crucial notions those of truth-maker and ontological dependence. The general hypothesis is that such a framework, as opposed to the one inherited from Quine ("On What There Is"), is required in contemporary debates about the relations of constitution and identity for material objects, response-dependent properties, propositional attitudes, realization of mental properties and the perspectives of naturalism, propositional attitudes, and the fictive/figurative analysis of several discourses. The project will be developed both by studying the central notions required for the articulation of the framework, and by applying it to several salient contemporary debates in ontology, the aforementioned among them. | |
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| Project: | MODNET. FP6
Marie Curie Training Network in Model Theory and its Applications. (MRTN-CT-2004-512234). |
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| Period: | 2005-2008 | |
| MODNET
(Barcelona) Scientist in charge: |
Enrique Casanovas | |
| Goals: | This project is designed to promote training and research in model theory, a part of mathematical logic dealing with abstract structures (models), historically with connections to other areas of mathematics. The project will stimulate research on a broad range of problems central to model theory and provide a wealth of opportunities for interactions between model theorists and those working in other areas of mathematics and theoretical computer science. The reseach objectives are to produce major advances in the following topics: Pure model theory, Model theory of fields and applications, o-minimality and applications, Henselian fields, Simple groups of finite Morley rank, Model theory of groups and modules, Decidability issues and links to complexity theory, and Finite model theory and links to computer science. | |
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| Project: | Bounded forcing axioms and their applications. Integrated Action Spain-French (HF 2005-0044). | |
| Period: | 2006-2007 | |
| Spanish Scientist in charge: | Joan Bagaria | |
| Goals: | Study of generic absoluteness for several classes of forcing notions. Study of definable versions of large cardinals (Mahlo, Remarkable, Weakly-compact, etc.) and their place in the usual large-cardinal hierarchy. Applications of bounded forcing axioms in infinite combinatorics and Banach space theory. Study of the axiom Bounded Martin Maximum (BMM), with applications to the structure of H(omega_2). The consistency strength of BMM. In particular, decide whether BMM implies that every projective set is determined, or even that every projective set of real numbers is Lebesgue measurable. Elaborate a coherent interpretation of set theory that allows to provide a sound justification for the new axioms. | |
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| Project: | Ontology and Language. Integrated Action Spanish-German (HA2005-0020). | |
| Period: | 2006-2007 | |
| Spanish Scientist in charge: | Manuel Pérez Otero | |
| Goals: | Study and discussion of the interrelation between language and ontology, illustrated in a number of topics: rigidity of general terms; treatments of rigidity in second-order languages; epistemic transparency of possible worlds; two-dimensional semantics; arguments for four-dimensionalism about continuants; past objects and temporal parts; existential phrases and the proper characterisation of ontology; linguistic and philosophical arguments about the nature of property-like entities, based on nominalisation of predicative phrases. | |
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Research Projects - I+D (MEC)
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| Project: | The constitution of representational content. Semantic and epistemic aspects. ( MEDU, HUM2005-07539-C02-01/FISO) | |
| Period: | 2005-2008 | |
| Scientist in charge: | Manuel Pérez Otero | |
| Topics: | Compatibilism between externalist theses and rational-internalist intuitions (about meaning, knowledge, epistemic justification). Transparency of representational content. Non-reducibility of the referential semantic function. Discriminatory abilities required for knowledge and singular individuation. Development and application of Peacocke’s theory of concepts and apriority. Necessary conditions for the use of proper names and their transmission, relevant for the acquisition of knowledge by testimony. Relations between mental and linguistic representations. | |
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| Project: | Truth in Special Contexts (BFF2003-08335-C03-03 (DGI)) | |
| Period: | 2003-2006 | |
| Scientist in charge: | Josep Macià | |
| Topics: | This project will try to show that there is nothing genuinely special about the so called special contexts, like moral and aesthetical discourse, or even fiction. We will argue for the view that the features of truth and its cognates in 'normal' (i.e. descriptive or theoretical) discursive contexts also suffice to account for the use of such notions in so called special discourses. | |
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| Project: | Foundations of Semantics: non factual and non representational aspects of meaning. (HUM 2005-00761) | |
| Period: | 2005-2008 | |
| Scientist in charge: | Genoveva Martí | |
| Topics: | This project continues and deepens the research lines open in our previous project (BFF2002-02846). Our objectives are: (a) to argue that an adequate semantic theory of names, indexicals and definite descriptions should take into account functional and categorical aspects of meaning that are independent of truth-conditional contribution; (b) apply the conclusions of our previous project to the semantics of general terms and explore two opposed conceptions of their linguistic function: as names of abstract entities or as essentially classificatory terms; (c) continue our work on a non-factual interpretation of attitude reports. | |
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| Project: | Model Theory (MTM 2005-00203) | |
| Period: | 2005-2008 | |
| Contact scientist: | Enrique Casanovas | |
| Topics: | Boolean algebras; topological model theory; abstract Galois groups; stability and simple theories; equality-free first order logic; model theoretic algebra; ordered abelian groups; separably closed fields; set theory; cardinal functions; infinitistic combinatorics. | |
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| Project: | Foundations and Aplications of Set Theory. (MTM 2005-01025) | |
| Period: | 2005-2008 | |
| Scientist in charge: | Joan Bagaria | |
| Topics: | One of the goals of Set Theory is the discovery, study, and classification of new axioms. A mathematical statement that cannot be decided on the basis of the standard Zermelo-Fraenkel Set Theory with the Axiom of Choice (ZFC) must be decided by supplementing ZFC with additional axioms. Strong axioms of infinity or large-cardinal axioms allow us to gauge the power of the set-theoretic axioms by measuring their consistency strength. However, many important mathematical questions, like the Continuum Hypothesis, cannot be decided directly by the axioms of large cardinals. Fortunately, other classes of axioms have been thoroughly studied which allow to answer many questions that are left undecided by the axioms of large-cardinals. These are, most notably, the forcing axioms. They assert that certain statements that hold in some ideal extension of the universe of all sets, a so-called generic or forcing extension, are true. In the last few years, a variety of results have shown that many strong axioms of Set Theory, apparently very diverse, can be reformulated in a similar way, namely, as principles of generic absoluteness. Our project aims to contribute to the generic absoluteness program, whose goal is the classification of the set-theoretic axioms by characterizing them in terms of generic absoluteness, thus providing a uniform framework for their study both in terms of consistency strength and their mutual connections, while turning them into an efficient ready-made tool for their applications to other areas of Mathematics. | |
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Other Research Groups
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| Group: | Prometheus 21. | |
| Scientist in charge: | Manuel Medina | |
| Topics: | (Catalan version) (Spanish version) | |
| June 30, 2006 |
