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In [[computability theory]] and [[mathematical logic]] the '''Tarski–Kuratowski algorithm''' is a [[non-deterministic algorithm] [[Category:Mathematical logic hierarchies]] ...

...e term ''pre-ordered set'' is unambiguous, and is always synonymous with a mathematical hierarchy. The term ''hierarchy'' is used to stress a ''[[hierarchical]]'' ...os]].</ref> This is not just a pedantic claim; there are also mathematical hierarchies, in the general sense, that are not describable using set theory.{{Citation ...

| publisher = Assoc. Symbol. Logic, La Jolla, CA [[Category:Mathematical logic hierarchies]] ...

...cal logic)|structure]] whose elements satisfy some [[formula (mathematical logic)|formula]] in the [[first-order language]] of that structure. A [[Set (math ...resulting structure are classified in the [[analytical hierarchy]]. These hierarchies reveal many relationships between definability in this structure and [[comp ...

In [[mathematical logic]], the '''Borel hierarchy''' is a stratification of the [[Borel algebra]] g ...es of sets of small finite ranks are important in [[measure theory]] and [[Mathematical analysis|analysis]]. ...

{{Short description|Mathematical concept}}{{refimprove|date=August 2011}} ...that can be defined by a [[Well-formed formula|formula]] of [[First-order logic|first-order]] [[Peano arithmetic]]. The arithmetical sets are classified b ...

| series = Studies in Logic and the Foundations of Mathematics ...rsion Theory''] (p.151). Association for Symbolic Logic, ''Perspectives in Logic''</ref> ...

In the mathematical field of [[descriptive set theory]], a subset <math>A</math> of a [[Polish .../tx070901146p.pdf What is... a Woodin cardinal?]". Notices of the American Mathematical Society vol. 54, no. 9 (2007), p.1147.</ref> ...

...ella, Capturing relativized complexity classes without order, Mathematical Logic Quarterly 44 (1998), no.&nbsp;1, pp.&nbsp;109–122.</ref> This hierarchy is [[Category:Mathematical logic hierarchies]] ...

...t2=Monika |editor-last3=Weiermann |editor-first3=Andreas |series=Trends in Logic |volume=53 |doi=10.1007/978-3-030-30229-0_13|isbn=978-3-030-30228-3 }}</ref ==Reverse-mathematical calibration== ...

{{short description|Subfield of mathematical logic}} ...ras]] and [[Group action (mathematics)|group actions]], and [[mathematical logic]]. ...

...>P. G. Hinman, ''Recursion-Theoretic Hierarchies'' (p.89), Perspectives in Logic, 1978. Springer-Verlag Berlin Heidelberg, ISBN 3-540-07904-1.</ref> ...theory]], [[effective descriptive set theory]], and the study of [[theory (logic)|formal theories]] such as [[Peano arithmetic]]. ...

{{Short description|Concept in mathematical logic and set theory}} In [[mathematical logic]] and [[descriptive set theory]], the '''analytical hierarchy''' is an exte ...

...ases for Classes of Primitive Recursive Functions | journal = Mathematical Logic Quarterly | volume = 48 | pages = 93–104 | doi=10.1002/1521-3870(200201)48: ...theorems on recursively enumerable sets", ''[[Notre Dame Journal of Formal Logic]]'', 1962, Volume 3, Number 2, pp 65-74, {{doi|10.1305/ndjfl/1093957149}}.< ...

...<math>A</math>.<ref>D. Martin, H. G. Dales, ''Truth in Mathematics'', ch. "Mathematical Evidence", p.224. Oxford Science Publications, 1998.</ref> The assertion th ...Volume II | publisher=Cambridge University Press | series=Lecture Notes in Logic |isbn=9781139504249| date= December 2011 }} ...

...Post's theorem uses several concepts relating to [[Structure (mathematical logic)#Definable_relations|definability]] and [[recursion theory]]. This section ...definable in the language of Peano arithmetic. A [[formula (mathematical logic)|formula]] is said to be <math>\Sigma^{0}_m</math> if it is an existential ...

...eural networks]], and made significant contributions to the foundations of mathematical [[intuitionism]].<ref>{{Cite book |last=Jurafsky |first=Daniel |author-link ...leene |url=https://philpapers.org/rec/SHOTMW |journal=Bulletin of Symbolic Logic |volume=1 |issue=1 |pages=8–43 |doi=10.2307/420945}}</ref><ref>{{Citation | ...

...[arithmetical hierarchy]] and [[analytical hierarchy]] from [[mathematical logic]]. The union of the classes in the hierarchy is denoted '''PH'''. Unlike the arithmetic and analytic hierarchies, whose inclusions are known to be proper, it is an open question whether an ...

...were introduced in [[Prolog II]]. The first implementations of constraint logic programming were [[Prolog III]], [[CLP(R)]], and [[CHIP (programming langua Instead of logic programming, constraints can be mixed with [[functional programming]], [[te ...

...}} showed in 1982 that Goodstein's theorem is [[independence (mathematical logic)|unprovable]] in [[Peano axioms#Peano arithmetic as first-order theory|Pean ...math> can be calibrated by relating it to various standard ordinal-indexed hierarchies of functions, such as the functions <math>H_\alpha</math> in the [[Hardy hi ...