Matches in SemOpenAlex for { <https://semopenalex.org/work/W2122472424> ?p ?o ?g. }
Showing items 1 to 77 of
77
with 100 items per page.
- W2122472424 endingPage "198" @default.
- W2122472424 startingPage "188" @default.
- W2122472424 abstract "Monotone inductive definitions occur frequently throughout mathematical logic. The set of formulas in a given language and the set of consequences of a given axiom system are examples of (monotone) inductively defined sets. The class of Borel subsets of the continuum can be given by a monotone inductive definition. Kleene's inductive definition of recursion in a higher type functional (see [6]) is fundamental to modern recursion theory; we make use of it in §2. Inductive definitions over the natural numbers have been studied extensively, beginning with Spector [11]. We list some of the results of that study in §1 for comparison with our new results on inductive definitions over the continuum. Note that for our purposes the continuum is identified with the Baire space ω ω. It is possible to obtain simple inductive definitions over the continuum by introducing real parameters into inductive definitions over N —as in the definition of recursion in [5]. This is itself an interesting concept and is discussed further in [4]. These parametric inductive definitions, however, are in general weaker than the unrestricted set of inductive definitions, as is indicated below. In this paper we outline, for several classes of monotone inductive definitions over the continuum, solutions to the following characterization problems: (1) What is the class of sets which may be given by such inductive definitions ? (2) What is the class of ordinals which are the lengths of such inductive definitions ? These questions are made more precise below. Most of the results of this paper were announced in [2]." @default.
- W2122472424 created "2016-06-24" @default.
- W2122472424 creator A5057979748 @default.
- W2122472424 date "1976-03-01" @default.
- W2122472424 modified "2023-09-27" @default.
- W2122472424 title "Monotone inductive definitions over the continuum" @default.
- W2122472424 cites W1977654535 @default.
- W2122472424 doi "https://doi.org/10.1017/s0022481200051884" @default.
- W2122472424 hasPublicationYear "1976" @default.
- W2122472424 type Work @default.
- W2122472424 sameAs 2122472424 @default.
- W2122472424 citedByCount "5" @default.
- W2122472424 countsByYear W21224724242012 @default.
- W2122472424 countsByYear W21224724242021 @default.
- W2122472424 crossrefType "journal-article" @default.
- W2122472424 hasAuthorship W2122472424A5057979748 @default.
- W2122472424 hasConcept C105795698 @default.
- W2122472424 hasConcept C11413529 @default.
- W2122472424 hasConcept C118615104 @default.
- W2122472424 hasConcept C134306372 @default.
- W2122472424 hasConcept C154945302 @default.
- W2122472424 hasConcept C167729594 @default.
- W2122472424 hasConcept C168773036 @default.
- W2122472424 hasConcept C202444582 @default.
- W2122472424 hasConcept C21563000 @default.
- W2122472424 hasConcept C2524010 @default.
- W2122472424 hasConcept C2777212361 @default.
- W2122472424 hasConcept C2834757 @default.
- W2122472424 hasConcept C33923547 @default.
- W2122472424 hasConcept C41008148 @default.
- W2122472424 hasConcept C96488702 @default.
- W2122472424 hasConceptScore W2122472424C105795698 @default.
- W2122472424 hasConceptScore W2122472424C11413529 @default.
- W2122472424 hasConceptScore W2122472424C118615104 @default.
- W2122472424 hasConceptScore W2122472424C134306372 @default.
- W2122472424 hasConceptScore W2122472424C154945302 @default.
- W2122472424 hasConceptScore W2122472424C167729594 @default.
- W2122472424 hasConceptScore W2122472424C168773036 @default.
- W2122472424 hasConceptScore W2122472424C202444582 @default.
- W2122472424 hasConceptScore W2122472424C21563000 @default.
- W2122472424 hasConceptScore W2122472424C2524010 @default.
- W2122472424 hasConceptScore W2122472424C2777212361 @default.
- W2122472424 hasConceptScore W2122472424C2834757 @default.
- W2122472424 hasConceptScore W2122472424C33923547 @default.
- W2122472424 hasConceptScore W2122472424C41008148 @default.
- W2122472424 hasConceptScore W2122472424C96488702 @default.
- W2122472424 hasIssue "1" @default.
- W2122472424 hasLocation W21224724241 @default.
- W2122472424 hasOpenAccess W2122472424 @default.
- W2122472424 hasPrimaryLocation W21224724241 @default.
- W2122472424 hasRelatedWork W1139328126 @default.
- W2122472424 hasRelatedWork W131202625 @default.
- W2122472424 hasRelatedWork W138853701 @default.
- W2122472424 hasRelatedWork W1446478209 @default.
- W2122472424 hasRelatedWork W1480150249 @default.
- W2122472424 hasRelatedWork W1579817075 @default.
- W2122472424 hasRelatedWork W1589408343 @default.
- W2122472424 hasRelatedWork W1616014753 @default.
- W2122472424 hasRelatedWork W1619426761 @default.
- W2122472424 hasRelatedWork W1969682671 @default.
- W2122472424 hasRelatedWork W1970069956 @default.
- W2122472424 hasRelatedWork W2041590892 @default.
- W2122472424 hasRelatedWork W2085251311 @default.
- W2122472424 hasRelatedWork W2113343895 @default.
- W2122472424 hasRelatedWork W218854924 @default.
- W2122472424 hasRelatedWork W2295797734 @default.
- W2122472424 hasRelatedWork W2320368816 @default.
- W2122472424 hasRelatedWork W354202743 @default.
- W2122472424 hasRelatedWork W68314263 @default.
- W2122472424 hasRelatedWork W85549400 @default.
- W2122472424 hasVolume "41" @default.
- W2122472424 isParatext "false" @default.
- W2122472424 isRetracted "false" @default.
- W2122472424 magId "2122472424" @default.
- W2122472424 workType "article" @default.