Classes of structures with no intermediate isomorphism problems

We say that a theory $T$ is intermediate under effective reducibility if the isomorphism problems among its computable models is neither hyperarithmetic nor on top under effective reducibility. We prove that if an infinitary sentence $T$ is uniformly effectively dense, a property we define in the paper, then no extension of it is intermediate, at least when relativized to every oracle on a cone. As an application we show that no infinitary sentence whose models are all linear orderings is intermediate under effective reducibility relative to every oracle on a cone

The Veblen functions for computability theorists

We study the computability-theoretic complexity and proof-theoretic strength of the following statements: (1) "If X is a well-ordering, then so is epsilon_X", and (2) "If X is a well-ordering, then so is phi(alpha,X)", where alpha is a fixed computable ordinal and phi the two-placed Veblen function. For the former statement, we show that omega iterations of the Turing jump are necessary in the proof and that the statement is equivalent to ACA_0^+ over RCA_0. To prove the latter statement we need to use omega^alpha iterations of the Turing jump, and we show that the statement is equivalent to Pi^0_{omega^alpha}-CA_0. Our proofs are purely computability-theoretic. We also give a new proof of a result of Friedman: the statement "if X is a well-ordering, then so is phi(X,0)" is equivalent to ATR_0 over RCA_0.Comment: 26 pages, 3 figures, to appear in Journal of Symbolic Logi

Asteroseismology of red giant stars: the potential of dipole modes

Since the detection of non-radial solar-like oscillation modes in red giants with the CoRoT satellite, the interest in the asteroseismic properties of red giants and the link with their global properties and internal structure is increasing. Moreover, more and more precise data are being collected with the space-based telescopes CoRoT and {\it Kepler}. Particularly relevant has been the detection of mixed modes in a large number of G-K red giants. In this contribution we discuss the potential of these dipole mixed modes to provide information on core extra-mixing and transport of angular momentum.Comment: Conference proceedings, Liac-40: "Ageing low mass stars: from red giants to white dwarfs

Independence in computable algebra

We give a sufficient condition for an algebraic structure to have a computable presentation with a computable basis and a computable presentation with no computable basis. We apply the condition to differentially closed, real closed, and difference closed fields with the relevant notions of independence. To cover these classes of structures we introduce a new technique of safe extensions that was not necessary for the previously known results of this kind. We will then apply our techniques to derive new corollaries on the number of computable presentations of these structures. The condition also implies classical and new results on vector spaces, algebraically closed fields, torsion-free abelian groups and Archimedean ordered abelian groups.Comment: 24 page

CoRoT 102918586: a Gamma Dor pulsator in a short period eccentric eclipsing binary

Pulsating stars in eclipsing binary systems are powerful tools to test stellar models. Binarity enables to constrain the pulsating component physical parameters, whose knowledge drastically improves the input physics for asteroseismic studies. The study of stellar oscillations allows us, in its turn, to improve our understanding of stellar interiors and evolution. The space mission CoRoT discovered several promising objects suitable for these studies, which have been photometrically observed with unprecedented accuracy, but needed spectroscopic follow-up. A promising target was the relatively bright eclipsing system CoRoT 102918586, which turned out to be a double-lined spectroscopic binary and showed, as well, clear evidence of Gamma Dor type pulsations. We obtained phase resolved high-resolution spectroscopy with the Sandiford spectrograph at the McDonald 2.1m telescope and the FEROS spectrograph at the ESO 2.2m telescope. Spectroscopy yielded both the radial velocity curves and, after spectra disentangling, the component effective temperatures, metallicity and line-of-sight projected rotational velocities. The CoRoT light curve was analyzed with an iterative procedure, devised to disentangle eclipses from pulsations. We obtained an accurate determination of the system parameters, and by comparison with evolutionary models strict constraints on the system age. Finally, the residuals obtained after subtraction of the best fitting eclipsing binary model were analyzed to determine the pulsator properties. We achieved a quite complete and consistent description of the system. The primary star pulsates with typical {\gamma} Dor frequencies and shows a splitting in period which is consistent with high order g-mode pulsations in a star of the corresponding physical parameters. The value of the splitting, in particular, is consistent with pulsations in l = 1 modes.Comment: 12 pages, 10 figures. Accepted for publication in Astronomy and Astrophysic