Matches in SemOpenAlex for { <https://semopenalex.org/work/W2313121624> ?p ?o ?g. }
Showing items 1 to 84 of
84
with 100 items per page.
- W2313121624 abstract "The present discussion stems from the following specific problem in the theory of (linearly) ordered sets: let m be any infinite cardinal; is it true that every ordered set of power m has a family of mutually disjoint intervals which is also of power m? This problem is solved, completely or partially, for all except those m > No which are strongly inaccessible.2 The solution is negative for all regular cardinals which are not strongly inaccessible, and is positive for some singular cardinals. Whether it is positive for all singular cardinals we do not know; the statement that it is (proposition Q) proves to be equivalent to a certain hypothesis from the domain of cardinal arithmetic (proposition P) which somewhat resembles, but is weaker than, the generalized hypothesis of the continuum. In particular the solution is negative for every cardinal which is a power of 2. For strongly inaccessible cardinals > No the problem remains open. These results are presented in ?2. The results in this section have been obtained jointly with Alfred Tarski and are included here with his kind permission. Some related problems, and some questions concerning the inaccessible numbers, are discussed in ?3. ?4 is devoted to a few somewhat less closely related theorems on decompositions of sets. 1. In this section we recall some definitions and notation and make a few preliminary remarks.3 The cardinal number of an arbitrary set M is denoted by M; the cardinal number of the set of all ordinals less than any fixed ordinal 4 is given the special symbol A. For every ordinal a, ;f(a) denotes the least cardinal p such that Na can be expressed as the sum of p cardinals each K,,, holds for every a. It follows that if ,, = no (for any n and d) then d < cf(a) (since (01)I n=b). In particular, as deduced by J. Konig a half-century ago, we have that 2NO K, (since cf(cw) = 0). But it is" @default.
- W2313121624 created "2016-06-24" @default.
- W2313121624 creator A5090411121 @default.
- W2313121624 date "1952-11-01" @default.
- W2313121624 modified "2023-09-26" @default.
- W2313121624 title "On Intervals of Ordered Sets" @default.
- W2313121624 cites W1041951484 @default.
- W2313121624 cites W2312519588 @default.
- W2313121624 cites W944417333 @default.
- W2313121624 cites W951947580 @default.
- W2313121624 doi "https://doi.org/10.2307/1969653" @default.
- W2313121624 hasPublicationYear "1952" @default.
- W2313121624 type Work @default.
- W2313121624 sameAs 2313121624 @default.
- W2313121624 citedByCount "3" @default.
- W2313121624 crossrefType "journal-article" @default.
- W2313121624 hasAuthorship W2313121624A5090411121 @default.
- W2313121624 hasConcept C100643331 @default.
- W2313121624 hasConcept C111472728 @default.
- W2313121624 hasConcept C112698675 @default.
- W2313121624 hasConcept C114614502 @default.
- W2313121624 hasConcept C118615104 @default.
- W2313121624 hasConcept C134306372 @default.
- W2313121624 hasConcept C138885662 @default.
- W2313121624 hasConcept C144133560 @default.
- W2313121624 hasConcept C162838799 @default.
- W2313121624 hasConcept C177264268 @default.
- W2313121624 hasConcept C199360897 @default.
- W2313121624 hasConcept C2777152325 @default.
- W2313121624 hasConcept C2778408900 @default.
- W2313121624 hasConcept C2780129039 @default.
- W2313121624 hasConcept C33923547 @default.
- W2313121624 hasConcept C41008148 @default.
- W2313121624 hasConcept C41895202 @default.
- W2313121624 hasConcept C45340560 @default.
- W2313121624 hasConcept C89507440 @default.
- W2313121624 hasConcept C96488702 @default.
- W2313121624 hasConceptScore W2313121624C100643331 @default.
- W2313121624 hasConceptScore W2313121624C111472728 @default.
- W2313121624 hasConceptScore W2313121624C112698675 @default.
- W2313121624 hasConceptScore W2313121624C114614502 @default.
- W2313121624 hasConceptScore W2313121624C118615104 @default.
- W2313121624 hasConceptScore W2313121624C134306372 @default.
- W2313121624 hasConceptScore W2313121624C138885662 @default.
- W2313121624 hasConceptScore W2313121624C144133560 @default.
- W2313121624 hasConceptScore W2313121624C162838799 @default.
- W2313121624 hasConceptScore W2313121624C177264268 @default.
- W2313121624 hasConceptScore W2313121624C199360897 @default.
- W2313121624 hasConceptScore W2313121624C2777152325 @default.
- W2313121624 hasConceptScore W2313121624C2778408900 @default.
- W2313121624 hasConceptScore W2313121624C2780129039 @default.
- W2313121624 hasConceptScore W2313121624C33923547 @default.
- W2313121624 hasConceptScore W2313121624C41008148 @default.
- W2313121624 hasConceptScore W2313121624C41895202 @default.
- W2313121624 hasConceptScore W2313121624C45340560 @default.
- W2313121624 hasConceptScore W2313121624C89507440 @default.
- W2313121624 hasConceptScore W2313121624C96488702 @default.
- W2313121624 hasLocation W23131216241 @default.
- W2313121624 hasOpenAccess W2313121624 @default.
- W2313121624 hasPrimaryLocation W23131216241 @default.
- W2313121624 hasRelatedWork W1627118729 @default.
- W2313121624 hasRelatedWork W174656504 @default.
- W2313121624 hasRelatedWork W1965568860 @default.
- W2313121624 hasRelatedWork W1972957003 @default.
- W2313121624 hasRelatedWork W1980382395 @default.
- W2313121624 hasRelatedWork W1981811422 @default.
- W2313121624 hasRelatedWork W2002785477 @default.
- W2313121624 hasRelatedWork W2006781958 @default.
- W2313121624 hasRelatedWork W2015615060 @default.
- W2313121624 hasRelatedWork W2063885590 @default.
- W2313121624 hasRelatedWork W2068299567 @default.
- W2313121624 hasRelatedWork W2106105867 @default.
- W2313121624 hasRelatedWork W2315950575 @default.
- W2313121624 hasRelatedWork W2319187540 @default.
- W2313121624 hasRelatedWork W2321203921 @default.
- W2313121624 hasRelatedWork W29340183 @default.
- W2313121624 hasRelatedWork W2963592743 @default.
- W2313121624 hasRelatedWork W3016883859 @default.
- W2313121624 hasRelatedWork W3104038630 @default.
- W2313121624 hasRelatedWork W3196314919 @default.
- W2313121624 isParatext "false" @default.
- W2313121624 isRetracted "false" @default.
- W2313121624 magId "2313121624" @default.
- W2313121624 workType "article" @default.