1,720,976 research outputs found
Provability logic: models within models in Peano Arithmetic
Full text linkIn 1994 Jech gave a model-theoretic proof of Godel's second incompleteness theorem for Zermelo-Fraenkel set theory in the following form: ZF does not prove that ZF has a model. Kodarski showed that Jech's proof can be adapted to Peano Arithmetic with the role of models being taken by complete consistent extensions. In this note we take another step in the direction of replacing proof-theoretic by model-theoretic arguments. We show, without the need of formalizing the proof of the completeness theorem within PA, that the existence of a model of PA of complexity Sigma(0)(2) is independent of PA, where a model is identified with the set of formulas with parameters which hold in the model. Our approach is based on a new interpretation of the provability logic of Peano Arithmetic where rectangle phi is defined as the formalization of "phi is true in every Sigma(0)(2)-model"
Uniformly approachable functions and UA spaces
No full textA generalization of uniformly continuous map (uniformly approachable function) is sutdied, as well as the spaces where every continuous real valued function is UA (UA spaces). The latter concept generalizes the notion of Atsuji space largely studied in topology. Various examples, as well as critorion for UA are provided
The usefulness of botulinum toxin type-a in the treatment of chronic sixth ocular nerve palsy
No full textABSTRACT
Purpose. The purpose of the study was to evaluate the efficacy of botulinum toxin type A (BTX-A) injection in patients with acquired VI nerve palsy.
Methods. Twenty-eight patients (16 F and 12 M), mean age 36, 42 +/- 17, 79 DS; range 10-69 years with acquired VI nerve palsy, have been treated with BTX-A injection into the ipsilateral medial rectus, at least 6 months after onset.
At 6 months follow up, a paresis and a paralysis, were respectively diagnosed if the affected eye could be actively abducted or not, across the mid-line; a simple horizontal rectus muscle procedure was performed for the paresis whilst for the paralysis, both a horizontal and vertical muscle transportation procedure were required.
Results. A gradual physiological recovery of the lateral rectus muscle was observed in 9 (32%) patients (GROUP I) and surgical treatment was therefore unnecessary; the remaining 19 cases (68%), of wich 5 paresis (GROUP II) and 14 paralysis (GROUP III) underwent surgery and within 1 year were all restored to orthotropia.
Conclusion. Botulinum toxin type-A (BTX-A) injection is an invaluable tool in the differential diagnosis between paresis versus paralysis of the VIth nerve, allowing the correct choice of surgical procedure.
Keywords: chronic acquired VI nerve palsy, botulinum toxin type-
New Surgical Intervention for the Weakening of the Inferior Oblique Muscle: Equatorial Scleral Anchor
No full textPurpose: To evaluate the efficacy of a new surgical technique in reducing inferior oblique muscle overaction. Methods: Anterior transposition and myectomy of the inferior oblique muscle represent the gold- standard treatment in dissociated vertical deviation, including cases in which a simultaneous inferior oblique muscle overaction is also present. A new surgical procedure that consists of suturing the muscle to the sclera at the Gobin point with tendon sparing using a micro-incision to minimize the related tissue trauma and induce a faster recovery was developed. Results: Two of 8 patients with essential infant esotropia had a complete resolution of the elevation in adduction with no residual vertical imbalance. All patients experienced an improvement in lateral incomitance. Conclusions: The new "equatorial scleral anchor" surgical procedure gives a similarly good outcome when compared with the classic inferior oblique anterior transposition technique, with the advantages being simple, safe, reversible, and modular in terms of suturing
Uniform quasi components, thin spaces and compact separation
No full textWe prove that every complete metric space X that is thin (i.e., every closed subspace has connected uniform quasi components) has the compact separation property (for any two disjoint closed connected subspaces A and B of X there is a compact set K disjoint from A and B such that every neighbourhood of K disjoint from A and B separates A and B). The real line and all compact spaces are obviously thin. We show that a space is thin if and only if it does not contain a certain forbidden configuration. Finally we prove that every metric UA-space (see [Rend. Instit. Mat. Univ. Trieste 25 (1993) 23–56]) is thin. The UA-spaces form a class properly including the Atsuji spaces
Local connectedness and extension of uniformly continuous functions
No full textA metric space X is straight if for each finite cover of X by closed sets, and for each real valued function f on X, if f is uniformly continuous on each set of the cover, then f is uniformly continuous on the whole of X. The straight spaces have been studied in [A. Berarducci, D. Dikranjan, J. Pelant, An additivity theorem for uniformly continuous functions, Topology and its Applications 146–147 (2005) 339–352], which contains characterization of the straight spaces within the class of the locally connected spaces (they are the uniformly locally connected ones) and the class of the totally disconnected spaces (they coincide with the totally disconnected Atsuji spaces). We show that the completion of a straight space is straight and we characterize the dense straight subspaces of a straight space. In order to clarify further the relation between straightness and the level of local connectedness of the space we introduce two more intermediate properties between straightness and uniform local connectedness and we give various examples to distinguish them. One of these properties coincides with straightness for complete spaces and provides in this way a useful characterization of complete straight spaces in terms of the behaviour of the quasi-components of the space
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