Matches in SemOpenAlex for { <https://semopenalex.org/work/W3034016151> ?p ?o ?g. }
Showing items 1 to 95 of
95
with 100 items per page.
- W3034016151 abstract "The Axiom of Choice (AC for short) is the most (in)famous axiom of the usual foundations of mathematics, ZFC set theory. The (non-)essential use of AC in mathematics has been well-studied and thoroughly classified. Now, fragments of countable AC not provable in ZF have recently been used in Kohlenbach's higher-order Reverse Mathematics to obtain equivalences between closely related compactness and local-global principles. We continue this study and show that NCC, a weak choice principle provable in ZF and much weaker systems, suffices for many of these results. In light of the intimate connection between Reverse Mathematics and computability theory, we also study realisers for NCC, i.e. functionals that produce the choice functions claimed to exist by the latter from the other data. Our hubris of undertaking the hitherto underdeveloped study of the computational properties of (choice functions from) AC leads to interesting results. For instance, using Kleene's S1-S9 computation schemes, we show that various total realisers for NCC compute Kleene's $exists^3$, a functional that gives rise to full second-order arithmetic, and vice versa. By contrast, partial realisers for NCC should be much weaker, but establishing this conjecture remains elusive. By way of catharsis, we show that the Continuum Hypothesis (CH for short) is equivalent to the existence of a countably based partial realiser for NCC. The latter kind of realiser does not compute Kleene's $exists^3$ and is therefore strictly weaker than a total one." @default.
- W3034016151 created "2020-06-12" @default.
- W3034016151 creator A5007539743 @default.
- W3034016151 creator A5073669576 @default.
- W3034016151 date "2020-05-30" @default.
- W3034016151 modified "2023-10-18" @default.
- W3034016151 title "The Axiom of Choice in Computability Theory and Reverse Mathematics, with a cameo for the Continuum Hypothesis" @default.
- W3034016151 cites W1505480266 @default.
- W3034016151 cites W1579817075 @default.
- W3034016151 cites W1584632423 @default.
- W3034016151 cites W1608084331 @default.
- W3034016151 cites W1608607427 @default.
- W3034016151 cites W2033831013 @default.
- W3034016151 cites W2045199616 @default.
- W3034016151 cites W2083391867 @default.
- W3034016151 cites W2126160338 @default.
- W3034016151 cites W2339460772 @default.
- W3034016151 cites W2615066822 @default.
- W3034016151 cites W2799398590 @default.
- W3034016151 cites W599690748 @default.
- W3034016151 cites W602306650 @default.
- W3034016151 cites W1983179900 @default.
- W3034016151 cites W1993508393 @default.
- W3034016151 doi "https://doi.org/10.48550/arxiv.2006.01614" @default.
- W3034016151 hasPublicationYear "2020" @default.
- W3034016151 type Work @default.
- W3034016151 sameAs 3034016151 @default.
- W3034016151 citedByCount "0" @default.
- W3034016151 crossrefType "posted-content" @default.
- W3034016151 hasAuthorship W3034016151A5007539743 @default.
- W3034016151 hasAuthorship W3034016151A5073669576 @default.
- W3034016151 hasBestOaLocation W30340161511 @default.
- W3034016151 hasConcept C10138342 @default.
- W3034016151 hasConcept C110729354 @default.
- W3034016151 hasConcept C111142201 @default.
- W3034016151 hasConcept C11413529 @default.
- W3034016151 hasConcept C118615104 @default.
- W3034016151 hasConcept C127753061 @default.
- W3034016151 hasConcept C134306372 @default.
- W3034016151 hasConcept C151797676 @default.
- W3034016151 hasConcept C152062344 @default.
- W3034016151 hasConcept C153046414 @default.
- W3034016151 hasConcept C162324750 @default.
- W3034016151 hasConcept C167729594 @default.
- W3034016151 hasConcept C177264268 @default.
- W3034016151 hasConcept C182306322 @default.
- W3034016151 hasConcept C199360897 @default.
- W3034016151 hasConcept C202444582 @default.
- W3034016151 hasConcept C24858836 @default.
- W3034016151 hasConcept C2524010 @default.
- W3034016151 hasConcept C2780990831 @default.
- W3034016151 hasConcept C33923547 @default.
- W3034016151 hasConcept C41008148 @default.
- W3034016151 hasConcept C556429856 @default.
- W3034016151 hasConcept C96488702 @default.
- W3034016151 hasConceptScore W3034016151C10138342 @default.
- W3034016151 hasConceptScore W3034016151C110729354 @default.
- W3034016151 hasConceptScore W3034016151C111142201 @default.
- W3034016151 hasConceptScore W3034016151C11413529 @default.
- W3034016151 hasConceptScore W3034016151C118615104 @default.
- W3034016151 hasConceptScore W3034016151C127753061 @default.
- W3034016151 hasConceptScore W3034016151C134306372 @default.
- W3034016151 hasConceptScore W3034016151C151797676 @default.
- W3034016151 hasConceptScore W3034016151C152062344 @default.
- W3034016151 hasConceptScore W3034016151C153046414 @default.
- W3034016151 hasConceptScore W3034016151C162324750 @default.
- W3034016151 hasConceptScore W3034016151C167729594 @default.
- W3034016151 hasConceptScore W3034016151C177264268 @default.
- W3034016151 hasConceptScore W3034016151C182306322 @default.
- W3034016151 hasConceptScore W3034016151C199360897 @default.
- W3034016151 hasConceptScore W3034016151C202444582 @default.
- W3034016151 hasConceptScore W3034016151C24858836 @default.
- W3034016151 hasConceptScore W3034016151C2524010 @default.
- W3034016151 hasConceptScore W3034016151C2780990831 @default.
- W3034016151 hasConceptScore W3034016151C33923547 @default.
- W3034016151 hasConceptScore W3034016151C41008148 @default.
- W3034016151 hasConceptScore W3034016151C556429856 @default.
- W3034016151 hasConceptScore W3034016151C96488702 @default.
- W3034016151 hasLocation W30340161511 @default.
- W3034016151 hasOpenAccess W3034016151 @default.
- W3034016151 hasPrimaryLocation W30340161511 @default.
- W3034016151 hasRelatedWork W14139091 @default.
- W3034016151 hasRelatedWork W15031382 @default.
- W3034016151 hasRelatedWork W1916728 @default.
- W3034016151 hasRelatedWork W29596644 @default.
- W3034016151 hasRelatedWork W33757802 @default.
- W3034016151 hasRelatedWork W45109062 @default.
- W3034016151 hasRelatedWork W45207373 @default.
- W3034016151 hasRelatedWork W45491602 @default.
- W3034016151 hasRelatedWork W52944341 @default.
- W3034016151 hasRelatedWork W57194850 @default.
- W3034016151 isParatext "false" @default.
- W3034016151 isRetracted "false" @default.
- W3034016151 magId "3034016151" @default.
- W3034016151 workType "article" @default.