Examples of using Model theory in English and their translations into Vietnamese
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Model theory= universal algebra+ logic.[1].
Ajdukiewicz's fields of research were model theory and the philosophy of science.
Model theory developed rapidly during the 1990s, and a more modern definition is provided by Wilfrid Hodges(1997).
The most prominent professional organization in the field of model theory is the Association for Symbolic Logic.
Model theory CRAH below the cooling capacity was 102 kWh compared to 750 kWh for the load capacity of IT equipment and lighting load combination.
A missing subdivision is computable model theory, but this can arguably be viewed as an independent subfield of logic.
Model theory has a different scope that encompasses more arbitrary theories, including foundational structures such as models of set theory. .
During the last several decades applied model theory has repeatedly merged with the more pure stability theory. .
Model theory in higher-order logics or infinitary logics is hampered by the fact that completeness and compactness do not in general hold for these logics.
The current research has proposed the following predictive model theory, Luong method,∆Tmax and fatigue life Nf are as follows.
If proof theory and model theory have been the foundation of mathematical logic, they have been but two of the four pillars of the subject.
It is also atool used in branches of mathematics including model theory, combinatorics, abstract algebra, and mathematical analysis.
In model theory, a branch of mathematical logic, two fields E and F are called elementarily equivalent if every mathematical statement that is true for E is also true for F and conversely.
The domain of a structure is an arbitrary set; it is also called the underlying set of the structure, its carrier(especially in universal algebra),or its universe(especially in model theory).
An example of a proof from geometric model theory is Hrushovski's proof of the Mordell- Lang conjecture for function fields.
Model theory recognizes and is intimately concerned with a duality: it examines semantical elements(meaning and truth) by means of syntactical elements(formulas and proofs) of a corresponding language.
The Source Book underrated the algebraic logic of De Morgan, Boole, Peirce, and Schröder, but devoted more pages to Skolem than to anyone other than Frege, and included Löwenheim(1915),the founding paper on model theory.
In a similar way to proof theory, model theory is situated in an area of interdisciplinarity among mathematics, philosophy, and computer science.
Finite model theory, which concentrates on finite structures, diverges significantly from the study of infinite structures in both the problems studied and the techniques used.
The result of this synthesis is called geometric model theory in this article(which is taken to include o-minimality, for example, as well as classical geometric stability theory). .
Informally, model theory can be divided into classical model theory, model theory applied to groups and fields, and geometric model theory.
In universal algebra and in model theory, a structure consists of a set along with a collection of finitary operations and relations that are defined on it.
In common usage, the words hypothesis, model, theory, and law have different interpretations and are at times used without precision, but in science they have very exact meanings.
A prolific author best known for his work on model theory, metamathematics, and algebraic logic, he also contributed to abstract algebra, topology, geometry, measure theory, mathematical logic, set theory, and analytic philosophy.
The ambition of geometric model theory is to provide a geography of mathematics by embarking on a detailed study of definable sets in various mathematical structures, aided by the substantial tools developed in the study of pure model theory.
In mathematical logic, and more specifically in model theory, an infinite structure M which is totally ordered by< is called an o-minimal structure if and only if every definable subset X⊂ M(with parameters taken from M) is a finite union of intervals and points.
The most often occurringtopics of the seminar are set theory and model theory in their philosophical connections, philosophy of mathematics in general, formalization of physical theories, such as special and general relativity within different logical frameworks.
For a given theory in model theory, a structure is called a model if it satisfies the defining axioms of that theory, although it is sometimes disambiguated as a semantic model when one discusses the notion in the more general setting of mathematical models. .
An important step in the evolution of classical model theory occurred with the birth of stability theory(through Morley's theorem on uncountably categorical theories and Shelah's classification program), which developed a calculus of independence and rank based on syntactical conditions satisfied by theories. .
The generation of models, theories and hypotheses.