Geodesic
On $E$-theorems
Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part VI, Tome 40 (1974), pp. 110-118

Voir la notice de l'article provenant de la source Math-Net.Ru

There are [1] many methods to construct for every proof of a sentence $\exists x A$ in Heyting (intuitionistic) arithmetic $HA$ [2] a term $t_p$ such that $A[t_p]$ is true (in some sence). It turns out that majority of these methods are equivalent: correspondent terms $t_p$ are convertible into one and the same natural number. This is proved here for three methods: (I) complete cut-elimination in the infinite formulation of $HA$ [3]; (II) recursive realizability [2]; (III) partial cut-elimination along the lines of Gentsen's 2-nd consistency proof [5]. [6] or normalization [7], [8]. It is shown that the process of cut-elimination by method (I) leads only to computation of values of terms associated with a given proof by methods (II) and (III). 
@article{ZNSL_1974_40_a12,
     author = {G. E. Mints},
     title = {On $E$-theorems},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {110--118},
     publisher = {mathdoc},
     volume = {40},
     year = {1974},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1974_40_a12/}
}
TY  - JOUR
AU  - G. E. Mints
TI  - On $E$-theorems
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 1974
SP  - 110
EP  - 118
VL  - 40
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_1974_40_a12/
LA  - ru
ID  - ZNSL_1974_40_a12
ER  - 
%0 Journal Article
%A G. E. Mints
%T On $E$-theorems
%J Zapiski Nauchnykh Seminarov POMI
%D 1974
%P 110-118
%V 40
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_1974_40_a12/
%G ru
%F ZNSL_1974_40_a12
G. E. Mints. On $E$-theorems. Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part VI, Tome 40 (1974), pp. 110-118. http://geodesic.mathdoc.fr/item/ZNSL_1974_40_a12/