A Model-Theoretic Approach to Ordinal Analysis

Autor:	Jeremy Avigad, Richard Sommer
Rok vydání:	1997
Předmět:	Nimber Discrete mathematics Philosophy Logic Large set (Ramsey theory) Ordinal arithmetic Contrast (statistics) Ordinal analysis Natural number Aleph number Ordinal notation FOS: Philosophy ethics and religion Mathematics
Zdroj:	Bulletin of Symbolic Logic. 3:17-52
ISSN:	1943-5894 1079-8986
Popis:	We describe a model-theoretic approach to ordinal analysis via the finite combinatorial notion of an α-large set of natural numbers. In contrast to syntactic approaches that use cut elimination, this approach involves constructing finite sets of numbers with combinatorial properties that, in nonstandard instances, give rise to models of the theory being analyzed. This method is applied to obtain ordinal analyses of a number of interesting subsystems of first- and second-order arithmetic.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8464a60707b72088631a747534444a80 https://doi.org/10.2307/421195 Zobrazit plný text záznamu