Recurrent longitudinally extensive transversal myelitis in a patient with Sjögren’s syndrome

Introduction. Longitudinally extensive transverse myelitis (LETM) is a transversal myelitis that extends through three or more vertebral segments in length. Case report. A 52- year-old woman was hospitalized due to pain in the lumbar region, difficulty in walking, hypoesthesia of the anogenital area and urinary retention. In the past medical history, two years earlier, the patient had been diagnosed with transversal myelitis confirmed by MRI of the cervical spine and six months earlier, the patient was diagnosed with primary Sjögren’s syndrome (SS). During the current hospitalization MRI of the spinal cord revealed extensive inflammatory lesions of almost the whole spinal cord. Lumbar puncture (LP) revealed mild pleocytosis and slightly increased protein level. Isoelectric focusing of cerebrospinal fluid (CSF) and serum proteins was normal. Visual evoked potentials were normal. Serological testing excluded acute viral infections. Corticosteroid therapy was applied with good therapeutic response. Control MRI revealed regression of pathological changes in the spinal cord. Conclusion. A wide range of disorders can cause LETM, but usually the first line diagnosis is neuromyelitis optica (NMO). Based on the detection of NMO immunoglobulin G in the serum of affected patients, a variety of allied disorders were grouped under the name of NMO spectrum disorders, including recurrent myelitis associated with LETM and myelitis associated with autoimmune disorders such as SS. There have been only a few cases reported in the literature with recurrent LETM associated with non-organ specific autoimmune disorder

Existentially Closed Models in the Framework of Arithmetic

We prove that the standard cut is definable in each existentially closed model of IΔ0 + exp by a (parameter free) П1–formula. This definition is optimal with respect to quantifier complexity and allows us to improve some previously known results on existentially closed models of fragments of arithmetic.Ministerio de Educación y Ciencia MTM2011–2684

Undecidable properties of self-affine sets and multi-tape automata

We study the decidability of the topological properties of some objects coming from fractal geometry. We prove that having empty interior is undecidable for the sets defined by two-dimensional graph-directed iterated function systems. These results are obtained by studying a particular class of self-affine sets associated with multi-tape automata. We first establish the undecidability of some language-theoretical properties of such automata, which then translate into undecidability results about their associated self-affine sets.Comment: 10 pages, v2 includes some corrections to match the published versio