Formally Real Fields
نویسندگان
چکیده
منابع مشابه
Counting Generalized Orders on Not Necessarily Formally Real Fields
The set of classical orderings of a field compatible with a given place from the field to the real numbers is known to be bijective with the set of homomorphisms from the value group of the place into the two element group. This fact is generalized here to the set of “generalized orders” compatible with an “extended absolute value,” i.e., an absolute value allowed to take the value ∞. The set o...
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We consider the signatures Σm = (0, 1,−,+, ·, ) of meadows and (Σm, s) of signed meadows. We give two complete axiomatizations of the equational theories of the real numbers with respect to these signatures. In the first case, we extend the axiomatization of zero-totalized fields by a single axiom scheme expressing formal realness; the second axiomatization presupposes an ordering. We apply the...
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In order to demonstrably satisfy hard real-time deadlines, a system must be predictable, and in particular the kernel must be predictable. In this paper we present and analyse a predictable kernel related to AORTA, a formal design language for hard real-time systems. The features of the kernel allow AORTA designs to be veriiably and semi-automatically implemented, and enable veriied guarantees ...
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In view of Albert's classical result that the dimension of each ordered, associative proper algebra over its center is necessarily infinite (cf. [1]), it seems not unlikely that a similar statement also holds for the rank of each proper formally real quasifield F, i.e. for the dimension of F over its kernel. Indeed, for some classes of ordered near fields and for ordered quasifields admitting a...
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ژورنال
عنوان ژورنال: Formalized Mathematics
سال: 2017
ISSN: 1898-9934,1426-2630
DOI: 10.1515/forma-2017-0024