A Proof-Theoretic Analysis of Theories for Stratified Inductive Definitions

Jäger, Gerhard; Probst, Dieter

doi:10.1007/978-3-319-10103-3_15

Cited by 2 publications

(3 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Transfinite stratification The equality

φ_{ɛ_{0}} (0) = | {\overset{ID}{true}}_{1} | = | {sans-serifSID}_{n} | = | {sans-serifSID}_{< ω} |

(with

n < ω

) established here still leaves the question open concerning the relationship of stratification to iteration. For this, we refer to where a generalisation of stratification to the transfinite gives an answer to it. Table captures line by line some aspects of this relationship and we refer again to for the meaning and characterisation of the last three rows.…”

Section: Discussionmentioning

confidence: 99%

“…For this, we refer to where a generalisation of stratification to the transfinite gives an answer to it. Table captures line by line some aspects of this relationship and we refer again to for the meaning and characterisation of the last three rows.…”

Section: Discussionmentioning

confidence: 99%

“…The theory

{SID}_{0}

is just

sans-serifPA

and the theory

{SID}_{1}

is essentially a weakening of

{ID}_{1}^{*}

where

({sans-serifID}^{*})

is further restricted in B to allow only arithmetical formulas. We shall investigate the theories

{SID}_{n}

of finitely stratified induction and refer for the next question on the treatment of transfinitely stratified induction to . In this note, we show how we can apply the proof theoretic technique of asymmetric interpretation very neatly in order to gain proof theoretic insight into this concept of stratified induction.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations