Everything Theory

As the Theory of Everything (TOE), IFA is the Study of Everything. On the IFA Internet, the acronym, TOE, also means the Totality of Existence. Hence, IFA provides the Standard Model of the TOE (Totality of Existence).

Ifa is the universal link that shows the interrelations of all fields and disciplines of knowledge.

For any form of knowledge, X, X theory is the study of X:

Mathematics and Abstract Structures

Theory	Object of Study (X)	Field / Domain	Definition (summary)
Group theory	Groups	Algebra	Study of algebraic structures with one associative operation and inverses.
Ring theory	Rings	Algebra	Study of sets with two operations (addition and multiplication).
Field theory	Fields	Algebra	Study of algebraic fields and their extensions.
Module theory	Modules	Algebra	Study of modules as generalizations of vector spaces.
Matrix theory	Matrices	Linear algebra	Study of matrices and their transformations.
Vector theory	Vectors	Linear algebra	Study of vectors, spaces, and linear operations.
Set theory	Sets	Foundations of math	Study of sets and membership relations.
Number theory	Numbers	Arithmetic	Study of integers and their properties.
Order theory	Orders	Algebra / Logic	Study of ordered sets and relations.
Lattice theory	Lattices	Algebra / Logic	Study of structures where every pair of elements has a meet and join.
Graph theory	Graphs	Discrete math	Study of vertices connected by edges.
Knot theory	Knots	Topology	Study of embeddings of circles in 3D space.
Topology (Topological theory)	Topological spaces	Geometry	Study of spatial properties preserved under deformation.
Measure theory	Measures	Analysis	Study of measures, integration, and measurable spaces.
Probability theory	Probabilities	Statistics	Study of random phenomena and distributions.
Combinatorics (Combinatorial theory)	Combinations	Discrete math	Study of counting, arrangement, and structure.
Category theory	Categories	Foundations / Meta-math	Study of objects and morphisms, unifying all of mathematics.
Representation theory	Representations	Algebra	Study of how algebraic structures act on vector spaces.
Operator theory	Operators	Functional analysis	Study of linear operators and their spectra.
Spectral theory	Spectra	Analysis / Physics	Study of eigenvalues and eigenfunctions.
Coding theory	Codes	Information science	Study of designing systems for data transmission and error correction.

Logic, Computation, and Lingustics

Theory	Object of Study (X)	Field / Domain	Definition (summary)
Model theory	Models	Mathematical logic	Study of the relationship between formal systems and their models.
Proof theory	Proofs	Logic	Study of formal proofs as mathematical objects.
Type theory	Types	Logic / Computer science	Study of systems classifying terms by their kinds.
Recursion theory	Recursive functions	Computability	Study of computable functions and decision problems.
Automata theory	Automata	Computer science	Study of abstract machines and computation.
Computation theory	Computations	Theoretical CS	Study of what can be computed.
Complexity theory	Computational complexity	CS / Math	Study of efficiency and difficulty of computational problems.
Algorithmic information theory	Information	CS / Math	Study of randomness and compressibility in data.
Formal language theory	Languages	CS / Linguistics	Study of syntactic structures and grammars.

Physics and Natural Sciences

Theory	Object of Study (X)	Field / Domain	Definition (summary)
Relativity theory	Relativistic systems	Physics	Study of space, time, and gravity.
Quantum theory	Quantum states	Physics	Study of microscopic phenomena governed by wavefunctions.
Field theory	Fields	Physics	Study of continuous fields like electromagnetic or gravitational.
String theory	Strings	Theoretical physics	Study of fundamental particles as one-dimensional strings.
Chaos theory	Chaotic systems	Nonlinear dynamics	Study of systems sensitive to initial conditions.
Thermodynamic theory	Heat and energy	Thermodynamics	Study of energy transfer and entropy.
Control theory	Control systems	Engineering / Physics	Study of regulation and feedback in systems.
Information theory	Information	Physics / Communication	Study of entropy, information, and transmission limits.
Electromagnetic theory	Electromagnetic fields	Physics	Study of electric and magnetic interactions.

Art, Humanities, and Applied, Social, and Decision Sciences

Theory	Object of Study (X)	Field / Domain	Definition (summary)
Art theory	Art	Aesthetics / Art Studies	Study of the nature, meaning, principles, and interpretation of art.
Humanities theory	Humanities	Humanities/Cultural Studies	Study of human culture, expression, interpretation, and meaning-making across literature, philosophy, history, and the arts.
Legal theory (Jurisprudence)	Law	Law/Legal Philosophy	Study of the nature, structure, sources, interpretation, and philosophy of law.
Game theory	Games (strategic interactions)	Economics/CS	Study of rational decision-making among interacting agents.
Decision theory	Decisions	Economics/ Psychology	Study of choices under risk and uncertainty.
Utility theory	Utility	Economics	Study of preference, value, and satisfaction optimization.
Network theory	Networks	Systems science	Study of interconnected nodes and their interactions.
Queuing theory	Queues	Operations research	Study of waiting lines, service systems, and resource allocation.
System theory	Systems	Systems science	Study of complex systems composed of interacting parts.
Information theory (social)	Information	Communication/ Sociology	Study of encoding, transmission, and interpretation of information among agents.
Learning theory	Learning	Education/AI/ Psychology	Study of how humans or machines acquire, update, and organize knowledge.

Philosophical and Conceptual Theories

Theory	Object of Study (X)	Field / Domain	Definition (summary)
Knowledge theory (Epistemology)	Knowledge	Philosophy	Study of knowledge, justification, and belief.
Truth theory	Truth	Philosophy / Logic	Study of the nature and correspondence of truth.
Value theory (Axiology)	Value	Philosophy	Study of ethics, aesthetics, and worth.
Relational theory	Relations	Metaphysics / Logic	Study of how relations constitute reality.
Complexity theory (general)	Complexity	Systems science	Study of emergence and adaptive order.
Meaning theory (Semantics)	Meaning	Linguistics / Philosophy	Study of meaning, reference, and interpretation.
Concept theory	Concepts	Cognitive science	Study of mental representations and categorization.

All these are encoded in IfaLang as energyforms/energyfields, with Energy revealed as the ToE Pattern and Universal Structure of Knowledge as a whole.

Every “theory” abstracts an entity (the X – energyform) and studies its relations, transformations, and properties.

Ifa Operations, Ifa Functions, and Ifa Mappings

In IFABOK, IfaRelation is the relational universe where all kinds of relations, operations, mappings, and functions, including binary operations and related concepts like arity, reside as conscious entities. Discover how Ifanary relations encompasses n-ary relations and n-ary operations in Mathematics and Computing.

Mathematical Framework Insights

Delve into the comprehensive meta-structure that supports unified theories in IFA Mathematics.