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{{Short description|Branch of mathematics}} ...t define the theories via the [[Landweber exact functor theorem]]. Typical theories it studies include: [[complex K-theory]], [[elliptic cohomology]], [[Morava ...

{{Short description|Decidable theory of equality}} ...ils/mathematicallogi00jdon | page=240 | chapter=Chapter 13: Some Decidable Theories}}</ref> ...

...e between elements. For example, if <code>f</code> is a function on values of type <code>Person</code>, it must be the case that for two <code>Person</co ...ypetheory.org/book/ |access-date=2023-09-13 |website=Homotopy Type Theory |language=en}}</ref> ...

...e notion is most important for countable [[first-order logic|first-order]] theories. ...er Lessmann, [https://doi.org/10.1007%2Fs001530100126 ''A primer of simple theories'']</ref> Despite this, the literature still widely refers to the Ryll-Nardz ...

...theories of bounded arithmetic as formal systems capturing various levels of feasible reasoning (see below). ...Arithmetic|journal=Bibliopolis, Naples, Italy, 1986.}}</ref> and a number of other logicians. ...

|title=Four Dimensional Holomorphic Theories |journal=Notices of the International Congress of Chinese Mathematicians ...

{{Short description|Theorem pertaining to the ontology of quantum mechanics}} ...2012. It has particular significance for how one may interpret the nature of the [[quantum state]]. ...

...rt description|Set of all true first-order statements about the arithmetic of natural numbers}} ...dard model]] of the [[Peano axioms]] in the [[Signature (logic)|language]] of the first-order Peano axioms. ...

{{short description|Feature of a typed formal language that builds new types from old ones}} ...[[type theory]], a '''type constructor''' is a feature of a typed [[formal language]] that builds new types from old ones. [[Basic type]]s are considered to be ...

...if it is of cardinality α and a unary relation is represented by a subset of cardinality β. The usual notation is <math>(\omega_2,\omega_1)\twoheadright ...ω₁-[[Erdős cardinal]]. Hans-Dieter Donder showed a weak version of the reverse implication: if CC is not only consistent but actually holds, t ...

| programming language = [[C++]] ...', also known as the '''Z3 Theorem Prover''', is a [[satisfiability modulo theories]] (SMT) solver developed by [[Microsoft]].<ref>{{Cite web |url=http://lim.u ...

...eory]], without substantially weakening the [[axiom of comprehension|axiom of unrestricted comprehension]]. ...volving the membership relation <math>\varepsilon</math>. Then, the axioms of DEST posit a set <math>A = \{ x | \phi(x)\}</math> such that <math>x \varep ...

.../modules.pdf|journal=Annals of Pure and Applied Logic|series=SPECIAL ISSUE|language=en|volume=26|issue=2|pages=149–213|doi=10.1016/0168-0072(84)90014-9|doi-acc ...'pp-''n''-formula''' is a formula in the language of (right) ''R''-modules of the form ...

{{Short description|A class of "well-behaved" models in set theory}} ...b>¹-proof theory, p. 206</ref> as a strengthening of the notion of ω-model. In contrast to the notation for set-theoretic properties named by ...

...ionality-journal.org/papers/compositionality-1-1/|journal=Compositionality|language=en|volume=1|pages=1|doi=10.32408/compositionality-1-1|arxiv=1801.05798|issn ...= Attempt of an axiomatic foundation of quantum mechanics and more general theories VI| journal = Communications in Mathematical Physics| date = 1971| doi = 10 ...

...rt to extend [[Yang–Mills theory]], which provides a universal description of the fundamental interactions, to describe [[Gravitation|gravity]]. ...avity]], which is a formulation of (classical) gravitation in the language of [[geometric algebra]]. Nor should it be confused with [[Kaluza–Klein theory ...

..., who have mostly opted for [[differential geometry]] approaches like that of the related [[gauge gravitation theory]]. ...field equations. These principles lead to the introduction of a new pair of linear functions, the position-gauge field and the rotation-gauge field. A ...

...egrees of freedom]]. Ghosts ensure '''mathematical consistency''' in gauge theories. If a given theory is self-consistent by the introduction of ghosts, these states are labeled "good". Good ghosts are [[Virtual particle ...

...tree automaton|finite-tree automata]] to infinite trees or as an extension of [[ω-automata|infinite-word automata]] to infinite trees. ...wo successors. It has been further observed that tree automata and logical theories are closely connected and it allows decision problems in logic to be reduce ...

{{Short description|Principle of classical logic}} ...nal logic]], '''import-export''' is a name given to the propositional form of [[Exportation (logic)|Exportation]]: ...