Matches in SemOpenAlex for { <https://semopenalex.org/work/W2308117615> ?p ?o ?g. }
Showing items 1 to 98 of
98
with 100 items per page.
- W2308117615 abstract "This paper provides some counterexamples to Cantor's contributions to the foundations of Set Theory. The first counterexample forces Cantor's Diagonal Method (DM) to yield one of the numbers in the target list. To study this anomaly, and given that for the DM to work the list of numbers have to be written down, the set of numbers that can be represented using positional fractional notation, $mathbb{W}$, is properly characterized. It is then shown that $mathbb{W}$ is not isomorphic to $mathbb{R}$, meaning that results obtained from the application of the DM to $mathbb{W}$ in order to derive properties of $mathbb{R}$ are not valid. It is then shown that Cantor's DM for a generic list of reals can be forced to yield one of the numbers of the list, thus invalidating Cantor's result that infers the non-denumerability of $mathbb{R}$ from the application of the DM to $mathbb{W}$. Cantor's Theorem about the different cardinalities of a set and its power set is then questioned, and by means of another counterexample we show that the theorem does not actually hold for infinite sets. After analyzing all these results, it is shown that the current notion of cardinality for infinite sets does not depend on the size of the sets, but rather on the representation chosen for them. Following this line of thought, the concept of model as a framework for the construction of the representation of a set is introduced, and a theorem showing that an infinite set can be well-ordered if there is a proper model for it is proven. To reiterate that the cardinality of a set does not determine whether the set can be well-ordered, a set of cardinality $aleph_{0}^{aleph_{0}}$ is proven to be equipollent to the set of natural numbers $mathbb{N}$. The paper concludes with an analysis of the cardinality of the ordinal numbers, for which a representation of cardinality $aleph_{0}^{aleph_{0}}$ is proposed." @default.
- W2308117615 created "2016-06-24" @default.
- W2308117615 creator A5073398838 @default.
- W2308117615 date "2014-04-24" @default.
- W2308117615 modified "2023-09-27" @default.
- W2308117615 title "Counterexamples to Cantorian Set Theory" @default.
- W2308117615 cites W1512373780 @default.
- W2308117615 cites W1544540238 @default.
- W2308117615 cites W1967678995 @default.
- W2308117615 cites W2023164309 @default.
- W2308117615 cites W2026762798 @default.
- W2308117615 cites W2086166831 @default.
- W2308117615 cites W2126160338 @default.
- W2308117615 cites W2796578679 @default.
- W2308117615 hasPublicationYear "2014" @default.
- W2308117615 type Work @default.
- W2308117615 sameAs 2308117615 @default.
- W2308117615 citedByCount "1" @default.
- W2308117615 countsByYear W23081176152014 @default.
- W2308117615 crossrefType "posted-content" @default.
- W2308117615 hasAuthorship W2308117615A5073398838 @default.
- W2308117615 hasConcept C100643331 @default.
- W2308117615 hasConcept C110729354 @default.
- W2308117615 hasConcept C114614502 @default.
- W2308117615 hasConcept C118615104 @default.
- W2308117615 hasConcept C124101348 @default.
- W2308117615 hasConcept C130367717 @default.
- W2308117615 hasConcept C138885662 @default.
- W2308117615 hasConcept C142399903 @default.
- W2308117615 hasConcept C162838799 @default.
- W2308117615 hasConcept C177264268 @default.
- W2308117615 hasConcept C17744445 @default.
- W2308117615 hasConcept C199360897 @default.
- W2308117615 hasConcept C199539241 @default.
- W2308117615 hasConcept C2524010 @default.
- W2308117615 hasConcept C2776359362 @default.
- W2308117615 hasConcept C2778408900 @default.
- W2308117615 hasConcept C33923547 @default.
- W2308117615 hasConcept C36605576 @default.
- W2308117615 hasConcept C41008148 @default.
- W2308117615 hasConcept C41895202 @default.
- W2308117615 hasConcept C45357846 @default.
- W2308117615 hasConcept C70654966 @default.
- W2308117615 hasConcept C87117476 @default.
- W2308117615 hasConcept C94375191 @default.
- W2308117615 hasConcept C94625758 @default.
- W2308117615 hasConceptScore W2308117615C100643331 @default.
- W2308117615 hasConceptScore W2308117615C110729354 @default.
- W2308117615 hasConceptScore W2308117615C114614502 @default.
- W2308117615 hasConceptScore W2308117615C118615104 @default.
- W2308117615 hasConceptScore W2308117615C124101348 @default.
- W2308117615 hasConceptScore W2308117615C130367717 @default.
- W2308117615 hasConceptScore W2308117615C138885662 @default.
- W2308117615 hasConceptScore W2308117615C142399903 @default.
- W2308117615 hasConceptScore W2308117615C162838799 @default.
- W2308117615 hasConceptScore W2308117615C177264268 @default.
- W2308117615 hasConceptScore W2308117615C17744445 @default.
- W2308117615 hasConceptScore W2308117615C199360897 @default.
- W2308117615 hasConceptScore W2308117615C199539241 @default.
- W2308117615 hasConceptScore W2308117615C2524010 @default.
- W2308117615 hasConceptScore W2308117615C2776359362 @default.
- W2308117615 hasConceptScore W2308117615C2778408900 @default.
- W2308117615 hasConceptScore W2308117615C33923547 @default.
- W2308117615 hasConceptScore W2308117615C36605576 @default.
- W2308117615 hasConceptScore W2308117615C41008148 @default.
- W2308117615 hasConceptScore W2308117615C41895202 @default.
- W2308117615 hasConceptScore W2308117615C45357846 @default.
- W2308117615 hasConceptScore W2308117615C70654966 @default.
- W2308117615 hasConceptScore W2308117615C87117476 @default.
- W2308117615 hasConceptScore W2308117615C94375191 @default.
- W2308117615 hasConceptScore W2308117615C94625758 @default.
- W2308117615 hasLocation W23081176151 @default.
- W2308117615 hasOpenAccess W2308117615 @default.
- W2308117615 hasPrimaryLocation W23081176151 @default.
- W2308117615 hasRelatedWork W1424698467 @default.
- W2308117615 hasRelatedWork W1482930854 @default.
- W2308117615 hasRelatedWork W1514076924 @default.
- W2308117615 hasRelatedWork W1973737783 @default.
- W2308117615 hasRelatedWork W1976365164 @default.
- W2308117615 hasRelatedWork W2015329281 @default.
- W2308117615 hasRelatedWork W2046805782 @default.
- W2308117615 hasRelatedWork W2051169511 @default.
- W2308117615 hasRelatedWork W2053946714 @default.
- W2308117615 hasRelatedWork W2081430538 @default.
- W2308117615 hasRelatedWork W2090437514 @default.
- W2308117615 hasRelatedWork W2090775178 @default.
- W2308117615 hasRelatedWork W2107232728 @default.
- W2308117615 hasRelatedWork W2323366404 @default.
- W2308117615 hasRelatedWork W2369300920 @default.
- W2308117615 hasRelatedWork W2391198733 @default.
- W2308117615 hasRelatedWork W2396217566 @default.
- W2308117615 hasRelatedWork W2768251629 @default.
- W2308117615 hasRelatedWork W2917349651 @default.
- W2308117615 hasRelatedWork W3151833102 @default.
- W2308117615 isParatext "false" @default.
- W2308117615 isRetracted "false" @default.
- W2308117615 magId "2308117615" @default.
- W2308117615 workType "article" @default.