Martin Bays
McMaster University
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Publication
Featured researches published by Martin Bays.
Bulletin of The London Mathematical Society | 2014
Martin Bays; Bradd Hart; Tapani Hyttinen; Meeri Kesälä; Jonathan Kirby
We show that the excellence axiom in the definition of Zilbers quasiminimal excellent classes is redundant, in that it follows from the other axioms. This substantially simplifies a number of categoricity proofs.
Bulletin of The London Mathematical Society | 2011
Martin Bays; Boris Zilber
An automatic degaussing circuit for a color picture tube (CPT) capable of automatically degaussing the CPT when a power conservation mode is released in a monitor having a power conservation function. The degaussing circuit includes a degaussing coil for eliminating electromagnetic waves produced from the CPT, a power conservation mode detecting section for detecting the release of the power conservation mode in accordance with a power conservation mode signal of the CPT inputted thereto and providing a degaussing control signal for controlling the operation of the degaussing coil if the release of the power conservation mode is detected, and a degaussing coil driving section for driving the degaussing coil for a predetermined time in accordance with the degaussing control signal when the power conservation mode is released.
Bulletin of The London Mathematical Society | 2010
Martin Bays; Jonathan Kirby; A. J. Wilkie
We prove the analogue of Schanuels conjecture for raising to the power of an exponentially transcendental real number. All but countably many real numbers are exponentially transcendental. We also give a more general result for several powers in a context which encompasses the complex case.
Algebra & Number Theory | 2018
Martin Bays; Jonathan Kirby
We give a construction of quasiminimal fields equipped with pseudo-analytic maps, generalising Zilbers pseudo-exponential function. In particular we construct pseudo-exponential maps of simple abelian varieties, including pseudo-
Transactions of the American Mathematical Society | 2014
Martin Bays; Philipp Habegger
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Transactions of the American Mathematical Society | 2017
Martin Bays; Martin Hils; Rahim Moosa
-functions for elliptic curves. We show that the complex field with the corresponding analytic function is isomorphic to the pseudo-analytic version if and only the appropriate version of Schanuels conjecture is true and the corresponding version of the strong exponential-algebraic closedness property holds. Moreover, we relativize the construction to build a model over a fairly arbitrary countable subfield and deduce that the complex exponential field is quasiminimal if it is exponentially-algebraically closed. This property asks only that the graph of exponentiation have non-trivial intersection with certain algebraic varieties but does not require genericity of these points. Furthermore Schanuels conjecture is not required as a condition for quasiminimality.
International Mathematics Research Notices | 2014
Martin Bays; Misha Gavrilovich; Martin Hils
Let C be an irreducible algebraic curve defined over a number field and inside an algebraic torus of dimension at least 3 . We partially answer a question posed by Levin on points on C for which a non-trivial power lies again on C . Our results have connections to Zilbers Conjecture on Intersections with Tori and yield to methods arising in transcendence theory and the theory of o-minimal structures.
arXiv: Logic | 2013
Martin Bays; Jonathan Kirby
Motivated by possible applications to meromorphic dynamics, and generalising known properties of difference-closed fields, this paper studies the theory CCMA of compact complex manifolds with a generic automorphism. It is shown that while CCMA does admit geometric elimination of imaginaries, it cannot eliminate imaginaries outright: a counterexample to 3-uniqueness in CCM is exhibited. Finite-dimensional types are investigated and it is shown, following the approach of Pillay and Ziegler, that the canonical base property holds in CCMA. As a consequence the Zilber dichotomy is deduced: finite-dimensional types of SU-rank one are either one-based or almost internal to the fixed field. In addition, a general criterion for stable embeddedness in TA (when it exists) is established, and used to determine the full induced structure of CCMA on projective varieties, simple nonalgebraic complex tori, and simply connected nonalgebraic strongly minimal manifolds.
Journal of The Institute of Mathematics of Jussieu | 2018
Martin Bays; Bradd Hart; Anand Pillay
arXiv: Logic | 2015
Martin Bays; Jonathan Kirby