FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2899353103> ?p ?o ?g. }

• W2899353103 abstract "IIn the context of a weak formal theory called Basic Intuitionistic Mathematics $mathsf{BIM}$, we study Brouwer's Fan Theorem and a strong negation of the Fan Theorem, Kleene's Alternative (to the Fan Theorem). We prove that the Fan Theorem is equivalent to contrapositions of a number of intuitionistically accepted axioms of countable choice and that Kleene's Alternative is equivalent to strong negations of these statements. We also discuss finite and infinite games and introduce a constructively useful notion of determinacy. We prove that the Fan Theorem is equivalent to the Intuitionistic Determinacy Theorem, saying that every subset of Cantor space is, in our constructively meaningful sense, determinate, and show that Kleene's Alternative is equivalent to a strong negation of a special case of this theorem. We then consider a uniform intermediate value theorem and a compactness theorem for classical propositional logic, and prove that the Fan Theorem is equivalent to each of these theorems and that Kleene's Alternative is equivalent to strong negations of them. We end with a note on a possibly important statement, provable from principles accepted by Brouwer, that one might call a Strong Fan Theorem." @default.
• W2899353103 created "2018-11-09" @default.
• W2899353103 creator A5084987525 @default.
• W2899353103 date "2013-11-27" @default.
• W2899353103 modified "2023-09-27" @default.
• W2899353103 title "The Fan Theorem, its strong negation, and the determinacy of games" @default.
• W2899353103 cites W1483259227 @default.
• W2899353103 cites W1509083246 @default.
• W2899353103 cites W1556453281 @default.
• W2899353103 cites W1568204127 @default.
• W2899353103 cites W1569386536 @default.
• W2899353103 cites W1590304156 @default.
• W2899353103 cites W172736740 @default.
• W2899353103 cites W1966245774 @default.
• W2899353103 cites W1973446732 @default.
• W2899353103 cites W1977324591 @default.
• W2899353103 cites W1977940437 @default.
• W2899353103 cites W1979862983 @default.
• W2899353103 cites W198178058 @default.
• W2899353103 cites W1982061352 @default.
• W2899353103 cites W1996516260 @default.
• W2899353103 cites W2004219814 @default.
• W2899353103 cites W2023169465 @default.
• W2899353103 cites W2039705582 @default.
• W2899353103 cites W2047144334 @default.
• W2899353103 cites W2057179252 @default.
• W2899353103 cites W2057631483 @default.
• W2899353103 cites W2062677359 @default.
• W2899353103 cites W2067028747 @default.
• W2899353103 cites W2118633760 @default.
• W2899353103 cites W2121042707 @default.
• W2899353103 cites W2134101218 @default.
• W2899353103 cites W2136762285 @default.
• W2899353103 cites W2139319952 @default.
• W2899353103 cites W2149374024 @default.
• W2899353103 cites W2321234531 @default.
• W2899353103 cites W2335408379 @default.
• W2899353103 cites W2466999195 @default.
• W2899353103 cites W2588855338 @default.
• W2899353103 cites W2898273547 @default.
• W2899353103 cites W561202933 @default.
• W2899353103 cites W56723072 @default.
• W2899353103 cites W966006768 @default.
• W2899353103 hasPublicationYear "2013" @default.
• W2899353103 type Work @default.
• W2899353103 sameAs 2899353103 @default.
• W2899353103 citedByCount "0" @default.
• W2899353103 crossrefType "posted-content" @default.
• W2899353103 hasAuthorship W2899353103A5084987525 @default.
• W2899353103 hasConcept C110729354 @default.
• W2899353103 hasConcept C118615104 @default.
• W2899353103 hasConcept C134306372 @default.
• W2899353103 hasConcept C137891326 @default.
• W2899353103 hasConcept C146147875 @default.
• W2899353103 hasConcept C151797676 @default.
• W2899353103 hasConcept C153046414 @default.
• W2899353103 hasConcept C154945302 @default.
• W2899353103 hasConcept C167729594 @default.
• W2899353103 hasConcept C171636804 @default.
• W2899353103 hasConcept C177264268 @default.
• W2899353103 hasConcept C180937797 @default.
• W2899353103 hasConcept C194886279 @default.
• W2899353103 hasConcept C199360897 @default.
• W2899353103 hasConcept C202444582 @default.
• W2899353103 hasConcept C2185349 @default.
• W2899353103 hasConcept C2524010 @default.
• W2899353103 hasConcept C2781302003 @default.
• W2899353103 hasConcept C33923547 @default.
• W2899353103 hasConcept C41008148 @default.
• W2899353103 hasConcept C45962547 @default.
• W2899353103 hasConcept C48540410 @default.
• W2899353103 hasConcept C58468513 @default.
• W2899353103 hasConceptScore W2899353103C110729354 @default.
• W2899353103 hasConceptScore W2899353103C118615104 @default.
• W2899353103 hasConceptScore W2899353103C134306372 @default.
• W2899353103 hasConceptScore W2899353103C137891326 @default.
• W2899353103 hasConceptScore W2899353103C146147875 @default.
• W2899353103 hasConceptScore W2899353103C151797676 @default.
• W2899353103 hasConceptScore W2899353103C153046414 @default.
• W2899353103 hasConceptScore W2899353103C154945302 @default.
• W2899353103 hasConceptScore W2899353103C167729594 @default.
• W2899353103 hasConceptScore W2899353103C171636804 @default.
• W2899353103 hasConceptScore W2899353103C177264268 @default.
• W2899353103 hasConceptScore W2899353103C180937797 @default.
• W2899353103 hasConceptScore W2899353103C194886279 @default.
• W2899353103 hasConceptScore W2899353103C199360897 @default.
• W2899353103 hasConceptScore W2899353103C202444582 @default.
• W2899353103 hasConceptScore W2899353103C2185349 @default.
• W2899353103 hasConceptScore W2899353103C2524010 @default.
• W2899353103 hasConceptScore W2899353103C2781302003 @default.
• W2899353103 hasConceptScore W2899353103C33923547 @default.
• W2899353103 hasConceptScore W2899353103C41008148 @default.
• W2899353103 hasConceptScore W2899353103C45962547 @default.
• W2899353103 hasConceptScore W2899353103C48540410 @default.
• W2899353103 hasConceptScore W2899353103C58468513 @default.
• W2899353103 hasLocation W28993531031 @default.
• W2899353103 hasOpenAccess W2899353103 @default.
• W2899353103 hasPrimaryLocation W28993531031 @default.
• W2899353103 hasRelatedWork W1560329072 @default.
• W2899353103 hasRelatedWork W1696059587 @default.

• next