Matches in SemOpenAlex for { <https://semopenalex.org/work/W4294597013> ?p ?o ?g. }
Showing items 1 to 68 of
68
with 100 items per page.
- W4294597013 abstract "Throughout the course of mathematical history, generalizations of previously understood concepts and structures have led to the fruitful development of the hierarchy of number systems, non-euclidean geometry, and many other epochal phases in mathematical progress. In the study of formalized theories of arithmetic, it is only natural to consider the extension from the standard model of Peano arithmetic, $langle mathbb{N},+,times,leq,0,1 rangle$, to non-standard models of arithmetic. The existence of non-standard models of Peano arithmetic provided motivation in the early $20^{th}$ century for a variety of questions in model theory regarding the classification of models up to isomorphism and the properties that non-standard models of Peano arithmetic have. This paper presents these questions and the necessary results to prove Tennenbaum's Theorem, which draws an explicit line between the properties of standard and non-standard models; namely, that no countable non-standard model of Peano arithmetic is recursive. These model-theoretic results have contributed to the foundational framework within which research programs developed by Skolem, Rosser, Tarski, Mostowski and others have flourished. While such foundational topics were crucial to active fields of research during the middle of the $20^{th}$ century, numerous open questions about models of arithmetic, and model theory in general, still remain pertinent to the realm of $21^{st}$ century mathematical discourse." @default.
- W4294597013 created "2022-09-05" @default.
- W4294597013 creator A5091488089 @default.
- W4294597013 date "2013-11-25" @default.
- W4294597013 modified "2023-09-30" @default.
- W4294597013 title "On Non-Standard Models of Peano Arithmetic and Tennenbaum's Theorem" @default.
- W4294597013 doi "https://doi.org/10.48550/arxiv.1311.6375" @default.
- W4294597013 hasPublicationYear "2013" @default.
- W4294597013 type Work @default.
- W4294597013 citedByCount "0" @default.
- W4294597013 crossrefType "posted-content" @default.
- W4294597013 hasAuthorship W4294597013A5091488089 @default.
- W4294597013 hasBestOaLocation W42945970131 @default.
- W4294597013 hasConcept C110729354 @default.
- W4294597013 hasConcept C111472728 @default.
- W4294597013 hasConcept C115624301 @default.
- W4294597013 hasConcept C118615104 @default.
- W4294597013 hasConcept C136119220 @default.
- W4294597013 hasConcept C138885662 @default.
- W4294597013 hasConcept C154945302 @default.
- W4294597013 hasConcept C180937797 @default.
- W4294597013 hasConcept C185592680 @default.
- W4294597013 hasConcept C202444582 @default.
- W4294597013 hasConcept C203436722 @default.
- W4294597013 hasConcept C2781302003 @default.
- W4294597013 hasConcept C33923547 @default.
- W4294597013 hasConcept C41008148 @default.
- W4294597013 hasConcept C61341680 @default.
- W4294597013 hasConcept C65148605 @default.
- W4294597013 hasConcept C8010536 @default.
- W4294597013 hasConcept C94375191 @default.
- W4294597013 hasConcept C97489613 @default.
- W4294597013 hasConceptScore W4294597013C110729354 @default.
- W4294597013 hasConceptScore W4294597013C111472728 @default.
- W4294597013 hasConceptScore W4294597013C115624301 @default.
- W4294597013 hasConceptScore W4294597013C118615104 @default.
- W4294597013 hasConceptScore W4294597013C136119220 @default.
- W4294597013 hasConceptScore W4294597013C138885662 @default.
- W4294597013 hasConceptScore W4294597013C154945302 @default.
- W4294597013 hasConceptScore W4294597013C180937797 @default.
- W4294597013 hasConceptScore W4294597013C185592680 @default.
- W4294597013 hasConceptScore W4294597013C202444582 @default.
- W4294597013 hasConceptScore W4294597013C203436722 @default.
- W4294597013 hasConceptScore W4294597013C2781302003 @default.
- W4294597013 hasConceptScore W4294597013C33923547 @default.
- W4294597013 hasConceptScore W4294597013C41008148 @default.
- W4294597013 hasConceptScore W4294597013C61341680 @default.
- W4294597013 hasConceptScore W4294597013C65148605 @default.
- W4294597013 hasConceptScore W4294597013C8010536 @default.
- W4294597013 hasConceptScore W4294597013C94375191 @default.
- W4294597013 hasConceptScore W4294597013C97489613 @default.
- W4294597013 hasLocation W42945970131 @default.
- W4294597013 hasLocation W42945970132 @default.
- W4294597013 hasOpenAccess W4294597013 @default.
- W4294597013 hasPrimaryLocation W42945970131 @default.
- W4294597013 hasRelatedWork W1561211379 @default.
- W4294597013 hasRelatedWork W1782959649 @default.
- W4294597013 hasRelatedWork W1865816693 @default.
- W4294597013 hasRelatedWork W1988393745 @default.
- W4294597013 hasRelatedWork W2790669912 @default.
- W4294597013 hasRelatedWork W3006263832 @default.
- W4294597013 hasRelatedWork W3100412477 @default.
- W4294597013 hasRelatedWork W3206674358 @default.
- W4294597013 hasRelatedWork W4206475822 @default.
- W4294597013 hasRelatedWork W885577916 @default.
- W4294597013 isParatext "false" @default.
- W4294597013 isRetracted "false" @default.
- W4294597013 workType "article" @default.