Matches in SemOpenAlex for { <https://semopenalex.org/work/W3100247314> ?p ?o ?g. }
Showing items 1 to 79 of
79
with 100 items per page.
- W3100247314 abstract "Reverse mathematics is a program in the foundations of mathematics. It provides an elegant classification in which the majority of theorems of ordinary mathematics fall into only five categories, based on the “big five” logical systems. Recently, a lot of effort has been directed toward finding exceptional theorems, that is, those which fall outside the big five. The so-called reverse mathematics zoo is a collection of such exceptional theorems (and their relations). It was previously shown that a number of uniform versions of the zoo theorems, that is, where a functional computes the objects stated to exist, fall in the third big five category, arithmetical comprehension, inside Kohlenbach’s higher-order reverse mathematics. In this paper, we extend and refine these previous results. In particular, we establish analogous results for recent additions to the reverse mathematics zoo, thus establishing that the latter disappear at the uniform level. Furthermore, we show that the aforementioned equivalences can be proved using only intuitionistic logic. Perhaps most surprisingly, these explicit equivalences are extracted from nonstandard equivalences in Nelson’s internal set theory, and we show that the nonstandard equivalence can be recovered from the explicit ones. Finally, the following zoo theorems are studied in this paper: Π10G (existence of uniformly Π10-generics), FIP (finite intersection principle), 1-GEN (existence of 1-generics), OPT (omitting partial types principle), AMT (atomic model theorem), SADS (stable ascending or descending sequence), AST (atomic model theorem with subenumerable types), NCS (existence of noncomputable sets), and KPT (Kleene–Post theorem that there exist Turing incomparable sets)." @default.
- W3100247314 created "2020-11-23" @default.
- W3100247314 creator A5073669576 @default.
- W3100247314 date "2018-01-01" @default.
- W3100247314 modified "2023-09-25" @default.
- W3100247314 title "Refining the Taming of the Reverse Mathematics Zoo" @default.
- W3100247314 cites W1485672136 @default.
- W3100247314 cites W1574049752 @default.
- W3100247314 cites W1967629533 @default.
- W3100247314 cites W2023021577 @default.
- W3100247314 cites W2045383980 @default.
- W3100247314 cites W2069787050 @default.
- W3100247314 cites W2099102402 @default.
- W3100247314 cites W2132134695 @default.
- W3100247314 cites W2170311001 @default.
- W3100247314 cites W2593449741 @default.
- W3100247314 cites W2603470071 @default.
- W3100247314 cites W2963358042 @default.
- W3100247314 cites W3098373946 @default.
- W3100247314 cites W3099017129 @default.
- W3100247314 cites W4232277851 @default.
- W3100247314 doi "https://doi.org/10.1215/00294527-2018-0015" @default.
- W3100247314 hasPublicationYear "2018" @default.
- W3100247314 type Work @default.
- W3100247314 sameAs 3100247314 @default.
- W3100247314 citedByCount "3" @default.
- W3100247314 countsByYear W31002473142019 @default.
- W3100247314 countsByYear W31002473142020 @default.
- W3100247314 countsByYear W31002473142021 @default.
- W3100247314 crossrefType "journal-article" @default.
- W3100247314 hasAuthorship W3100247314A5073669576 @default.
- W3100247314 hasBestOaLocation W31002473142 @default.
- W3100247314 hasConcept C118615104 @default.
- W3100247314 hasConcept C127413603 @default.
- W3100247314 hasConcept C127753061 @default.
- W3100247314 hasConcept C136119220 @default.
- W3100247314 hasConcept C145420912 @default.
- W3100247314 hasConcept C146978453 @default.
- W3100247314 hasConcept C167729594 @default.
- W3100247314 hasConcept C183140480 @default.
- W3100247314 hasConcept C202444582 @default.
- W3100247314 hasConcept C2524010 @default.
- W3100247314 hasConcept C33923547 @default.
- W3100247314 hasConcept C64543145 @default.
- W3100247314 hasConceptScore W3100247314C118615104 @default.
- W3100247314 hasConceptScore W3100247314C127413603 @default.
- W3100247314 hasConceptScore W3100247314C127753061 @default.
- W3100247314 hasConceptScore W3100247314C136119220 @default.
- W3100247314 hasConceptScore W3100247314C145420912 @default.
- W3100247314 hasConceptScore W3100247314C146978453 @default.
- W3100247314 hasConceptScore W3100247314C167729594 @default.
- W3100247314 hasConceptScore W3100247314C183140480 @default.
- W3100247314 hasConceptScore W3100247314C202444582 @default.
- W3100247314 hasConceptScore W3100247314C2524010 @default.
- W3100247314 hasConceptScore W3100247314C33923547 @default.
- W3100247314 hasConceptScore W3100247314C64543145 @default.
- W3100247314 hasIssue "4" @default.
- W3100247314 hasLocation W31002473141 @default.
- W3100247314 hasLocation W31002473142 @default.
- W3100247314 hasLocation W31002473143 @default.
- W3100247314 hasLocation W31002473144 @default.
- W3100247314 hasLocation W31002473145 @default.
- W3100247314 hasOpenAccess W3100247314 @default.
- W3100247314 hasPrimaryLocation W31002473141 @default.
- W3100247314 hasRelatedWork W1557945163 @default.
- W3100247314 hasRelatedWork W1983348982 @default.
- W3100247314 hasRelatedWork W1985218657 @default.
- W3100247314 hasRelatedWork W2093689493 @default.
- W3100247314 hasRelatedWork W2096753949 @default.
- W3100247314 hasRelatedWork W2327285180 @default.
- W3100247314 hasRelatedWork W2946979626 @default.
- W3100247314 hasRelatedWork W2963341196 @default.
- W3100247314 hasRelatedWork W3106133691 @default.
- W3100247314 hasRelatedWork W4249580765 @default.
- W3100247314 hasVolume "59" @default.
- W3100247314 isParatext "false" @default.
- W3100247314 isRetracted "false" @default.
- W3100247314 magId "3100247314" @default.
- W3100247314 workType "article" @default.