On locally finite varieties of Heyting algebras

For every $n \in \mathbb{N}$, we construct a variety of Heyting algebras, whose $n$-generated free algebra is finite but whose $(n+1)$-generated free algebra is infinite

Logics of left variable inclusion and Płonka sums of matrices

The paper aims at studying, in full generality, logics defined by imposing a variable inclusion condition on a given logic ⊢. We prove that the description of the algebraic counterpart of the left variable inclusion companion of a given logic ⊢ is related to the construction of Płonka sums of the matrix models of ⊢. This observation allows to obtain a Hilbert-style axiomatization of the logics of left variable inclusion, to describe the structure of their reduced models, and to locate them in the Leibniz hierarchy

Bi-intermediate logics of trees and co-trees

A bi-Heyting algebra validates the G\"odel-Dummett axiom $(p\to q)\vee (q\to p)$ iff the poset of its prime filters is a disjoint union of co-trees (i.e., order duals of trees). Bi-Heyting algebras of this kind are called bi-G\"odel algebras and form a variety that algebraizes the extension $\mathsf{bi}$-$\mathsf{LC}$ of bi-intuitionistic logic axiomatized by the G\"odel-Dummett axiom. In this paper we initiate the study of the lattice $\Lambda(\mathsf{bi}$-$\mathsf{LC})$ of extensions of $\mathsf{bi}$-$\mathsf{LC}$. We develop the methods of Jankov-style formulas for bi-G\"odel algebras and use them to prove that there are exactly continuum many extensions of $\mathsf{bi}$-$\mathsf{LC}$. We also show that all these extensions can be uniformly axiomatized by canonical formulas. Our main result is a characterization of the locally tabular extensions of $\mathsf{bi}$-$\mathsf{LC}$. We introduce a sequence of co-trees, called the finite combs, and show that a logic in $\mathsf{bi}$-$\mathsf{LC}$ is locally tabular iff it contains at least one of the Jankov formulas associated with the finite combs. It follows that there exists the greatest non-locally tabular extension of $\mathsf{bi}$-$\mathsf{LC}$ and consequently, a unique pre-locally tabular extension of $\mathsf{bi}$-$\mathsf{LC}$. These results contrast with the case of the intermediate logic axiomatized by the G\"odel-Dummett axiom, which is known to have only countably many extensions, all of which are locally tabular

Amenable covers and integral foliated simplicial volume

In analogy with ordinary simplicial volume, we show that integral foliated simplicial volume of oriented closed connected aspherical n-manifolds that admit an open amenable cover of multiplicity at most n is zero. This implies that the fundamental groups of such manifolds have fixed price and are cheap as well as reproves some statements about homology growth

Platelet-rich plasma for regeneration of neural feedback pathways around dental implants: a concise review and outlook on future possibilities

published_or_final_versio

Adherence issues related to sublingual immunotherapy as perceived by allergists

Objectives: Sublingual immunotherapy (SLIT) is a viable alternative to subcutaneous immunotherapy to treat allergic rhinitis and asthma, and is widely used in clinical practice in many European countries. The clinical efficacy of SLIT has been established in a number of clinical trials and meta-analyses. However, because SLIT is self-administered by patients without medical supervision, the degree of patient adherence with treatment is still a concern. The objective of this study was to evaluate the perception by allergists of issues related to SLIT adherence. Methods: We performed a questionnaire-based survey of 296 Italian allergists, based on the adherence issues known from previous studies. The perception of importance of each item was assessed by a VAS scale ranging from 0 to 10. Results: Patient perception of clinical efficacy was considered the most important factor (ranked 1 by 54% of allergists), followed by the possibility of reimbursement (ranked 1 by 34%), and by the absence of side effects (ranked 1 by 21%). Patient education, regular follow-up, and ease of use of SLIT were ranked first by less than 20% of allergists. Conclusion: These findings indicate that clinical efficacy, cost, and side effects are perceived as the major issues influencing patient adherence to SLIT, and that further improvement of adherence is likely to be achieved by improving the patient information provided by prescribers. © 2010 Scurati et al, publisher and licensee Dove Medical Press Ltd

A MATSUMOTO–MOSTOW RESULT FOR ZIMMER’S COCYCLES OF HYPERBOLIC LATTICES

none2noFollowing the philosophy behind the theory of maximal representations, we introduce the volume of a Zimmer’s cocycle Γ × X → PO° (n, 1), where Γ is a torsion-free (non-)uniform lattice in PO° (n, 1), with n > 3, and X is a suitable standard Borel probability Γ-space. Our numerical invariant extends the volume of representations for (non-)uniform lattices to measurable cocycles and in the uniform setting it agrees with the generalized version of the Euler number of self-couplings. We prove that our volume of cocycles satisfies a Milnor–Wood type inequality in terms of the volume of the manifold Γℍn. Additionally this invariant can be interpreted as a suitable multiplicative constant between bounded cohomology classes. This allows us to define a family of measurable cocycles with vanishing volume. The same interpretation enables us to characterize maximal cocycles for being cohomologous to the cocycle induced by the standard lattice embedding via a measurable map X → PO° (n, 1) with essentially constant sign. As a by-product of our rigidity result for the volume of cocycles, we give a different proof of the mapping degree theorem. This allows us to provide a complete characterization of maps homotopic to local isometries between closed hyperbolic manifolds in terms of maximal cocycles. In dimension n = 2, we introduce the notion of Euler number of measurable cocycles associated to a closed surface group and we show that it extends the classic Euler number of representations. Our Euler number agrees with the generalized version of the Euler number of self-couplings up to a multiplicative constant. Imitating the techniques developed in the case of the volume, we show a Milnor–Wood type inequality whose upper bound is given by the modulus of the Euler characteristic of the associated closed surface. This gives an alternative proof of the same result for the generalized version of the Euler number of self-couplings. Finally, using the interpretation of the Euler number as a multiplicative constant between bounded cohomology classes, we characterize maximal cocycles as those which are cohomologous to the one induced by a hyperbolization.mixedMoraschini M.; Savini A.Moraschini M.; Savini A

A matsumoto-mostrow result for zimmer's cocycles of hyperbolic lattices

Following the philosophy behind the theory of maximal representations, we introduce the volume of a Zimmer's cocycle Gamma x X -> PO degrees (n, 1), where Gamma is a torsion-free (non-)uniform lattice in PO degrees (n, 1), with n > 3, and X is a suitable standard Borel probability Gamma-space. Our numerical invariant extends the volume of representations for (non-)uniform lattices to measurable cocycles and in the uniform setting it agrees with the generalized version of the Euler number of self-couplings. We prove that our volume of cocycles satisfies a Milnor-Wood type inequality in terms of the volume of the manifold Gamma\(n). Additionally this invariant can be interpreted as a suitable multiplicative constant between bounded cohomology classes. This allows us to define a family of measurable cocycles with vanishing volume. The same interpretation enables us to characterize maximal cocycles for being cohomologous to the cocycle induced by the standard lattice embedding via a measurable map X -> PO degrees (n, 1) with essentially constant sign. As a by-product of our rigidity result for the volume of cocycles, we give a different proof of the mapping degree theorem. This allows us to provide a complete characterization of maps homotopic to local isometries between closed hyperbolic manifolds in terms of maximal cocycles. In dimension n = 2, we introduce the notion of Euler number of measurable cocycles associated to a closed surface group and we show that it extends the classic Euler number of representations. Our Euler number agrees with the generalized version of the Euler number of self-couplings up to a multiplicative constant. Imitating the techniques developed in the case of the volume, we show a Milnor-Wood type inequality whose upper bound is given by the modulus of the Euler characteristic of the associated closed surface. This gives an alternative proof of the same result for the generalized version of the Euler number of self-couplings. Finally, using the interpretation of the Euler number as a multiplicative constant between bounded cohomology classes, we characterize maximal cocycles as those which are cohomologous to the one induced by a hyperbolization

Multiplicative constants and maximal measurable cocycles in bounded cohomology

none2noMultiplicative constants are a fundamental tool in the study of maximal representations. In this paper, we show how to extend such notion, and the associated framework, to measurable cocycles theory. As an application of this approach, we define and study the Cartan invariant for measurable PU(m, 1)-cocycles of complex hyperbolic lattices.mixedMoraschini M.; Savini A.Moraschini M.; Savini A