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20 relations: Łoś–Vaught test, Cambridge University Press, Complete theory, Critical point (set theory), Ehrenfeucht–Fraïssé game, First-order logic, Large cardinal, Löwenheim–Skolem theorem, Mathematical logic, Model theory, Non-standard model of arithmetic, Peano axioms, Rational number, Real number, Set theory, Signature (logic), Structure (mathematical logic), Substructure, Theory (mathematical logic), Total order.
Łoś–Vaught test
In model theory, a branch of mathematical logic, the Łoś–Vaught test is a criterion for a theory to be complete, unable to be augmented without becoming inconsistent.
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Cambridge University Press
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
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Complete theory
In mathematical logic, a theory is complete if, for every formula in the theory's language, that formula or its negation is demonstrable.
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Critical point (set theory)
In set theory, the critical point of an elementary embedding of a transitive class into another transitive class is the smallest ordinal which is not mapped to itself.
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Ehrenfeucht–Fraïssé game
In the mathematical discipline of model theory, the Ehrenfeucht–Fraïssé game (also called back-and-forth games) is a technique for determining whether two structures are elementarily equivalent.
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First-order logic
First-order logic—also known as first-order predicate calculus and predicate logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science.
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Large cardinal
In the mathematical field of set theory, a large cardinal property is a certain kind of property of transfinite cardinal numbers.
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Löwenheim–Skolem theorem
In mathematical logic, the Löwenheim–Skolem theorem, named for Leopold Löwenheim and Thoralf Skolem, states that if a countable first-order theory has an infinite model, then for every infinite cardinal number κ it has a model of size κ. The result implies that first-order theories are unable to control the cardinality of their infinite models, and that no first-order theory with an infinite model can have a unique model up to isomorphism.
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Mathematical logic
Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics.
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Model theory
In mathematics, model theory is the study of classes of mathematical structures (e.g. groups, fields, graphs, universes of set theory) from the perspective of mathematical logic.
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Non-standard model of arithmetic
In mathematical logic, a non-standard model of arithmetic is a model of (first-order) Peano arithmetic that contains non-standard numbers.
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Peano axioms
In mathematical logic, the Peano axioms, also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers presented by the 19th century Italian mathematician Giuseppe Peano.
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Rational number
In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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Set theory
Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.
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Signature (logic)
In logic, especially mathematical logic, a signature lists and describes the non-logical symbols of a formal language.
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Structure (mathematical logic)
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.
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Substructure
In mathematical logic, an (induced) substructure or (induced) subalgebra is a structure whose domain is a subset of that of a bigger structure, and whose functions and relations are the traces of the functions and relations of the bigger structure.
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Theory (mathematical logic)
In mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language.
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Total order
In mathematics, a linear order, total order, simple order, or (non-strict) ordering is a binary relation on some set X, which is antisymmetric, transitive, and a connex relation.
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