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abstract model theory is a generalization of model theory that studies the general properties of extensions of first-order logic and their models. Abstract
Abstract_model_theory
Theoretical framework
Conceptual models range in type from the more concrete, such as the mental image of a familiar physical object, to the formal generality and abstractness of mathematical
Conceptual_model
Informative representation of an entity
from Latin modulus, 'a measure'. Models can be divided into physical models (e.g. a ship model) and abstract models (e.g. a set of mathematical equations
Model
Formal system in mathematical logic
only abstract logic that is countably compact and has Löwenheim number ω. Abstract algebraic logic – Aspect of mathematical logic Abstract model theory Löwenheim
Abstract_logic
Theorem in mathematical logic
known result of what later became known as abstract model theory, the basic notion of which is an abstract logic; the more general notion of an institution
Lindström's_theorem
Area of mathematical logic
In mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing
Model_theory
Theoretical computer used for defining a model of computation
purely theoretical reasons as well as models for real-world computer systems. In the theory of computation, abstract machines are often used in thought experiments
Abstract_machine
Process of generalization
play an important role in the theory of general semantics originated by Alfred Korzybski. Anatol Rapoport wrote, "Abstracting is a mechanism by which an
Abstraction
Subfield of logic that studies the features common to all logical systems
An abstract model theory system axiomatized by Jon Barwise, a topological/categorical approach based on sketches (sometimes called categorical model theory)
Universal_logic
Mathematical model describing how an output of a function is computed given an input
more specifically in computability theory and computational complexity theory, a model of computation is a model that describes how an output of a mathematical
Model_of_computation
Aspect of mathematical logic
Andréka, István Németi and others. Abstract algebra Algebraic logic Abstract model theory Hierarchy (mathematics) Model theory Variety (universal algebra) Universal
Abstract_algebraic_logic
Branch of mathematics that studies the properties of groups
In abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known
Group_theory
Process of extracting the underlying essence of a mathematical concept
detail Generalization Abstract thinking Abstract logic Abstract algebraic logic Abstract model theory Abstract nonsense Concept Mathematical maturity Bertrand
Abstraction_(mathematics)
Mapping of mathematical formulas to a particular meaning
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
Structure (mathematical logic)
Structure_(mathematical_logic)
In model theory, a discipline within mathematical logic, an abstract elementary class, or AEC for short, is a class of models with a partial order similar
Abstract_elementary_class
Supposition or system of ideas intended to explain something
Measure theory — Model theory — Module theory — Morse theory — Nevanlinna theory — Number theory — Obstruction theory — Operator theory — Order theory — PCF
Theory
Branch of logic
Finite model theory is a subarea of model theory. Model theory is the branch of logic which deals with the relation between a formal language (syntax)
Finite_model_theory
Institutional theory and Institutional logic. In mathematical logic, institutional model theory generalizes a large portion of first-order model theory to an
Institutional_model_theory
Class of models in the behavioral sciences
Rational choice modeling refers to the use of decision theory (the theory of rational choice) as a set of guidelines to help understand economic and social
Rational_choice_model
Branch of mathematics that studies sets
(set theory) Elementary Theory of the Category of Sets Glossary of set theory List of set theory topics Relational model – borrows from set theory Structural
Set_theory
Concept in model theory
In model theory, interpretation of a structure M in another structure N (typically of a different signature) is a technical notion that approximates the
Interpretation_(model_theory)
Psychological theory of motivation
parallel Maslow's theory of a need hierarchy. However, Herzberg added a new dimension to this theory by proposing a two-factor model of motivation, based
Two-factor_theory
Academic subfield of computer science
science and mathematics, the theory of computation is the branch that deals with what problems can be solved on a model of computation using an algorithm
Theory_of_computation
Concept in model theory
In model theory, a first-order theory is called model complete if every embedding of its models is an elementary embedding. Equivalently, every first-order
Model_complete_theory
Type theory in logic and mathematics
intuition of (abstract) homotopy theory applies. This includes, among other lines of work, the construction of homotopical and higher-categorical models for such
Homotopy_type_theory
Concept in model theory
In model theory and related areas of mathematics, a type is an object that describes how a (real or possible) element or finite collection of elements
Type_(model_theory)
Set of sentences in a formal language
from the theory. A satisfiable theory is a theory that has a model. This means there is a structure M that satisfies every sentence in the theory. Any satisfiable
Theory_(mathematical_logic)
economy in microeconomics, and the standard model of a game in game theory. An equilibrium in an abstract economy generalizes both a Walrasian equilibrium
Abstract_economy
Concerned with the notion of stability in model theory
mathematical field of model theory, a theory is called stable if it satisfies certain combinatorial restrictions on its complexity. Stable theories are rooted in
Stable_theory
Branch of mathematics that studies abstract algebraic structures
Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of
Representation_theory
Approach to static program analysis
In computer science, abstract interpretation is a theory of sound approximation of the semantics of computer programs, based on monotonic functions over
Abstract_interpretation
Study of abstract machines and automata
Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them. It is a theory in theoretical
Automata_theory
As simple a model as possible, in model theory
mathematics, and in particular model theory, a prime model is a model that is as simple as possible. Specifically, a model P {\displaystyle P} is prime
Prime_model
Inclusion of one mathematical structure in another, preserving properties of interest
(a_{1},\ldots ,a_{n})\in R^{A}} . In model theory there is also a stronger notion of elementary embedding. In order theory, an embedding of partially ordered
Embedding
Tool used in structural semantics
desired object depends on the abstract power often connected to the subject. Analysing characters according to the actantial model enables a detailed breakdown
Actantial_model
Computation model defining an abstract machine
mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity
Turing_machine
Type of machine learning model
Chaining Large Language Model Prompts through Visual Programming". CHI Conference on Human Factors in Computing Systems Extended Abstracts. Association for Computing
Large_language_model
2004: Springer LNCS 3052 Abstract State Machines 2004 2003: Springer LNCS 2589 Abstract State Machines 2003: Advances in Theory and Practice 2003: TCS special
Abstract_state_machine
Description of a system using mathematical concepts and language
mathematical model is an abstract description of a concrete system using mathematical concepts and language. The process of developing a mathematical model is termed
Mathematical_model
(OWL) Abstract model theory Institutional model theory Universal logic J. A. Goguen; R. M. Burstall (1992), "Institutions: Abstract model theory for specification
Institution (computer science)
Institution_(computer_science)
Model in mathematical logic not isomorphic to the standard model
In model theory, a discipline within mathematical logic, a non-standard model is a model of a theory that is not isomorphic to the intended model (or standard
Non-standard_model
Fundamental unit of cognition
learned and innate concepts, concrete and abstract concepts, and natural and logical concepts. The classical theory holds that concepts are essentially definitions
Concept
Theory of brain function
predictive processing) is a theory of brain function which postulates that the brain is constantly generating and updating a "mental model" of the environment
Predictive_coding
Type of theory in mathematical logic
mathematical logic, a theory is categorical if it has exactly one model (up to isomorphism). Such a theory can be viewed as defining its model, uniquely characterizing
Categorical_theory
A mathematical object is an abstract concept arising in mathematics. Typically, a mathematical object can be a value that can be assigned to a symbol,
Mathematical_object
Type of infinite structure
In mathematical logic, and more specifically in model theory, an infinite structure ( M , < , … ) {\displaystyle (M,<,\dots )} that is totally ordered
O-minimal_theory
Abstract model
A data model is an abstract model that organizes elements of data and standardizes how they relate to one another and to the properties of real-world entities
Data_model
Systems theory in political science is a highly abstract, partly holistic view of politics, influenced by cybernetics. The adaptation of system theory to political
Systems theory in political science
Systems_theory_in_political_science
Linked node hierarchical data structure
In computer science, a tree is a widely used abstract data type that represents a hierarchical tree structure with a set of connected nodes. Each node
Tree_(abstract_data_type)
Model of (first-order) Peano arithmetic that contains non-standard numbers
can be proved in Zermelo–Fraenkel set theory that Goodstein's theorem holds in the standard model, so a model where Goodstein's theorem fails must be
Non-standard model of arithmetic
Non-standard_model_of_arithmetic
Philosophical theory attributed to Plato
Forms are various abstract ideals that exist even outside of human minds and that constitute the basis of reality. Thus, Plato's Theory of Forms is a type
Theory_of_forms
Mathematical construction
construction that appears mainly in abstract algebra and mathematical logic, in particular in model theory and set theory. An ultraproduct is the quotient
Ultraproduct
Mathematical term; concerning axioms used to derive theorems
nineteenth century. They included non-Euclidean geometry, Georg Cantor's abstract set theory, and Hilbert's revisionist axioms for Euclidean geometry. David Hilbert
Axiomatic_system
Study of programming languages via mathematical objects
connections with abstract interpretation, program verification, and model checking. Dana S. Scott. Outline of a mathematical theory of computation. Technical
Denotational_semantics
Concept in mathematics
model-theoretic means, a stronger notion is obtained: an extension T2 of a theory T1 is model-theoretically conservative if T1 ⊆ T2 and every model of
Conservative_extension
American computer scientist
contributions to fuzzy set theory. In the 1970s Goguen's work was one of the earliest approaches to the algebraic characterisation of abstract data types and he
Joseph_Goguen
Study of the semantics, or interpretations, of formal and natural languages
of model-theoretic semantics is Alfred Tarski's semantic theory of truth, based on his T-schema, and is one of the founding concepts of model theory. This
Semantics_(logic)
The categorical abstract machine (CAM) is a model of computation for programs that preserves the abilities of applicative, functional, or compositional
Categorical_abstract_machine
Theory of truth in the philosophy of language
A semantic theory of truth is a theory of truth in the philosophy of language which holds that truth is a property of sentences. The semantic conception
Semantic_theory_of_truth
Model theory concept
In model theory, a branch of mathematical logic, the spectrum of a theory is given by the number of isomorphism classes of models in various cardinalities
Spectrum_of_a_theory
Structure in mathematical logic
substructure. In model theory, the term "submodel" is often used as a synonym for substructure, especially when the context suggests a theory of which both
Substructure_(mathematics)
Theory of strings with supersymmetry
Superstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modeling them as vibrations of tiny
Superstring_theory
Mathematical study of the meaning of programming languages
theory, model theory, category theory, etc. It has close links with other areas of computer science such as programming language design, type theory,
Semantics (programming languages)
Semantics_(programming_languages)
In model theory, a subfield of mathematical logic, an atomic model is a model such that the complete type of every tuple is axiomatized by a single formula
Atomic model (mathematical logic)
Atomic_model_(mathematical_logic)
Mathematician, prolific contributor to homotopy theory
contributions to the theory of simplicial sets and simplicial methods in topology in general. In recognition of this, the usual closed model category structure
Daniel_Kan
First modern model of the atom
atom was discussed, and by the end of the century the leading model was the vortex theory of the atom, proposed by William Thomson (later Lord Kelvin)
Plum_pudding_model
Model for mathematical theories
In mathematical logic, and particularly in its subfield model theory, a saturated model is one that realizes as many complete types as may be "reasonably
Saturated_model
Standard system of axiomatic set theory
such sets. Thus the axioms of Zermelo–Fraenkel set theory refer only to pure sets and prevent its models from containing urelements (elements that are not
Zermelo–Fraenkel_set_theory
In model theory, a discipline within the field of mathematical logic, a tame abstract elementary class is an abstract elementary class (AEC) which satisfies
Tame abstract elementary class
Tame_abstract_elementary_class
Theory in the philosophy of perception
self-awareness including: emotion, self-reflection, ego, and theory. The theory of abstract and imaginary sense data operates on the tacit definition of
Sense_data
Existence and cardinality of models of logical theories
models, named after Leopold Löwenheim and Thoralf Skolem. The precise formulation is given below. It implies that if a countable first-order theory has
Löwenheim–Skolem_theorem
Formulation of matroids using closure operators
pregeometries, geometries, and abstract closure operators influence the structure of first-order models is called geometric stability theory. If V {\displaystyle
Pregeometry_(model_theory)
Branch of mathematics
points of X and the morphisms are paths. Abstract homotopy theory is an axiomatic approach to homotopy theory. Such axiomatization is useful for non-traditional
Homotopy_theory
Academic journal
Combustion Theory and Modelling is a bimonthly peer-reviewed scientific journal covering research on combustion. The editors-in-chief are Moshe Matalon
Combustion Theory and Modelling
Combustion_Theory_and_Modelling
Mathematical logic concept
Skolem's paradox is the apparent contradiction that a countable model of first-order set theory could contain an uncountable set. The paradox arises from part
Skolem's_paradox
Branch of computer science
abstract typed functional language. In 1978, Robin Milner introduces the Hindley–Milner type system inference algorithm for ML language. Type theory became
Programming_language_theory
Non-contradiction of a theory
theory is satisfiable if it has a model, i.e., there exists an interpretation under which all axioms in the theory are true. This is what consistent meant
Consistency
Field of knowledge
convergence), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of abstract objects that
Mathematics
Reasoning about equations with free variables
the founder of set theoretic model theory as a major branch of contemporary mathematical logic, also: Initiated abstract algebraic logic with relation
Algebraic_logic
Psychological theory of how thought can arise in two different ways
process theory focused in the field of social psychology in 1986. Their theory is called the elaboration likelihood model of persuasion. In their theory, there
Dual_process_theory
Theories in mathematical logic
first-order theory is given by a set of axioms in some language. This entry lists some of the more common examples used in model theory and some of their
List_of_first-order_theories
Study of rational collective decision-making
field is occasionally called voting theory. It is closely related to mechanism design, which uses game theory to model social choice with imperfect information
Social_choice_theory
of Kurepa's conjecture and two-cardinal conjectures in model theory, in Axiomatic Set Theory, Proc. Symp, in Pure Mathematics (13) pp. 383 – 390, 1967
List of statements independent of ZFC
List_of_statements_independent_of_ZFC
Fundamental theorem in mathematical logic
applies to any first-order theory: If T is such a theory, and φ is a sentence (in the same language) and every model of T is a model of φ, then there is a
Gödel's_completeness_theorem
Attraction of masses and energy
derive a model of gravity is based on action principles. This formulation represents the effects of gravity on a system in a mathematically abstract way.
Gravity
Formal system of logic
"simple" indicates that the underlying type theory is the theory of simple types, also called the simple theory of types. Leon Chwistek and Frank P. Ramsey
Higher-order_logic
Theory that discusses human intelligence from an epistemological perspective
Piaget's theory of cognitive development, or his genetic epistemology, is a comprehensive theory about the nature and development of human intelligence
Piaget's theory of cognitive development
Piaget's_theory_of_cognitive_development
Branch of biology
cancer modelling, neural nets, genetic networks, abstract categories in relational biology, metabolic-replication systems, category theory applications
Mathematical and theoretical biology
Mathematical_and_theoretical_biology
Mathematical model for deduction or proof systems
may have some basis in an abstract model. Often the formal system will be the basis for or even identified with a larger theory or field (e.g. Euclidean
Formal_system
Model of consciousness
Global workspace theory (GWT) is a cognitive architecture and theoretical framework for understanding consciousness and was first introduced in 1988 by
Global_workspace_theory
In set theory, an extender is a system of ultrafilters which represents an elementary embedding witnessing large cardinal properties. A nonprincipal ultrafilter
Extender_(set_theory)
Mathematical category with weak equivalences, fibrations and cofibrations
axioms relating them. These abstract from the category of topological spaces or of chain complexes (derived category theory). The concept was introduced
Model_category
Topics referred to by the same term
(disambiguation) Model City (disambiguation) Model School (disambiguation) Model Town (disambiguation) Mathematical model, an abstract description of a
Model_(disambiguation)
Finnish mathematical logician known for his contributions to set theory, model theory, logic and foundations of mathematics. He served as the vice-rector
Jouko_Väänänen
Physical theory with fields invariant under the action of local "gauge" Lie groups
four-potential, with the photon being the gauge boson. The Standard Model is a non-abelian gauge theory with the symmetry group U(1) × SU(2) × SU(3) and has a total
Gauge_theory
Aspect of consciousness research
consciousness. Sometimes the models are labeled theories of consciousness. Anil Seth defines such models as those that relate brain phenomena such as fast
Models_of_consciousness
Theory of categorization in psychology
Prototype theory is a theory of categorization in cognitive science, particularly in psychology and cognitive linguistics, in which there is a graded degree
Prototype_theory
Sociolinguistic model of code-switching
markedness model (sociolinguistic theory) proposed by Carol Myers-Scotton is one account of the social indexical motivation for code-switching. The model holds
Markedness_model
Method in mathematical logic
In mathematical logic, specifically in the discipline of model theory, the Fraïssé limit (also called the Fraïssé construction or Fraïssé amalgamation)
Fraïssé_limit
Thesis on the nature of computability
Elementary Number Theory". American Journal of Mathematics. 58 (2): 345–363. doi:10.2307/2371045. Retrieved 2026-02-24. An abstract of Church's paper
Church–Turing_thesis
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