CHAINS OF THEORIES AND COMPANIONABILITY

Download

index.pdf

Date

2015-11-01

Author

Kasal, Ozcan
Pierce, David

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

169
views

0
downloads

The theory of fields that are equipped with a countably infinite family of commuting derivations is not companionable, but if the axiom is added whereby the characteristic of the fields is zero, then the resulting theory is companionable. Each of these two theories is the union of a chain of companionable theories. In the case of characteristic 0, the model-companions of the theories in the chain form another chain, whose union is therefore the model-companion of the union of the original chain. However, in a signature with predicates, in all finite numbers of arguments, for linear dependence of vectors, the two-sorted theory of vector-spaces with their scalar-fields is companionable, and it is the union of a chain of companionable theories, but the model-companions of the theories in the chain are mutually inconsistent. Finally, the union of a chain of non-companionable theories may be companionable.

Subject Keywords

Model-theory, Fields

URI

https://hdl.handle.net/11511/65355

Journal

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

DOI

https://doi.org/10.1090/proc12789

Collections

Natural Sciences and Mathematics, Article

Suggestions

OpenMETU
Core

Scalar waves in spacetimes with closed timelike curves Buğdaycı, Necmi; Başkal, Sibel; Department of Physics (2005) The existence and -if exists- the nature of the solutions of the scalar wave equation in spacetimes with closed timelike curves are investigated. The general properties of the solutions on some class of spacetimes are obtained. Global monochromatic solutions of the scalar wave equation are obtained in flat wormholes of dimensions 2+1 and 3+1. The solutions are in the form of infinite series involving cylindirical and spherical wave functions and they are elucidated by the multiple scattering method. Explici...
On the deformation chirality of real cubic fourfolds Finashin, Sergey (Wiley, 2009-09-01) According to our previous results, the conjugacy class of the involution induced by the complex conjugation in the homology of a real non-singular cubic fourfold determines the fourfold tip to projective equivalence and deformation. Here, we show how to eliminate the projective equivalence and obtain a pure deformation classification, that is, how to respond to the chirality problem: which cubics are not deformation equivalent to their image under a mirror reflection. We provide an arithmetical criterion of...
Value sets of Lattes maps over finite fields Küçüksakallı, Ömer (Elsevier BV, 2014-10-01) We give an alternative computation of the value sets of Dickson polynomials over finite fields by using a singular cubic curve. Our method is not only simpler but also it can be generalized to the non-singular elliptic case. We determine the value sets of Lattes maps over finite fields which are rational functions induced by isogenies of elliptic curves with complex multiplication.
A SPINOR MODEL FOR QUANTUM COSMOLOGY DERELI, T; ONDER, M; TUCKER, RW (1994-03-31) The question of the interpretation of Wheeler-DeWitt solutions in the context of cosmological models is addressed by implementing the Hamiltonian constraint as a spinor wave equation in minisuperspace. We offer a relative probability interpretation based on a non-closed vector current in this space and a prescription for a parametrisation of classical solutions in terms of classical time. Such a prescription can accommodate classically degenerate metrics describing manifolds with signature change. The relat...
Galois structure of modular forms of even weight Gurel, E. (Elsevier BV, 2009-10-01) We calculate the equivariant Euler characteristics of powers of the canonical sheaf on certain modular curves over Z which have a tame action of a finite abelian group. As a consequence, we obtain information on the Galois module structure of modular forms of even weight having Fourier coefficients in certain ideals of rings of cyclotomic algebraic integers. (c) 2009 Elsevier Inc. All rights reserved.

Citation Formats

O. Kasal and D. Pierce, “CHAINS OF THEORIES AND COMPANIONABILITY,” PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, pp. 4937–4949, 2015, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/65355.