Transfinite ordinal numbers enter mathematical practice mainly via the method of definition by transfinite recursion. Outside of axiomatic set theory, there is a significant mathematical tradition in works recasting proofs by transfinite recursion in other terms, mostly with the intention of eliminating the ordinals from the proofs. Leaving aside the different motivations which lead each specific case, we investigate the mathematics of this action of proof transforming and we address the problem of formalising the philosophical notion of elimination which characterises this move.
Eliminating the Ordinals from Proofs. An Analysis of Transfinite Recursion
RIVELLO E
2014-01-01
Abstract
Transfinite ordinal numbers enter mathematical practice mainly via the method of definition by transfinite recursion. Outside of axiomatic set theory, there is a significant mathematical tradition in works recasting proofs by transfinite recursion in other terms, mostly with the intention of eliminating the ordinals from the proofs. Leaving aside the different motivations which lead each specific case, we investigate the mathematics of this action of proof transforming and we address the problem of formalising the philosophical notion of elimination which characterises this move.File in questo prodotto:
File | Dimensione | Formato | |
---|---|---|---|
Pre-proceedings PhML 2014.pdf
Accesso riservato
Tipo di file:
PREPRINT (PRIMA BOZZA)
Dimensione
248.55 kB
Formato
Adobe PDF
|
248.55 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.