Geodesic
Independence of the uniformity principle from Church's thesis in intuitionistic set theory
Izvestiya. Mathematics , Tome 77 (2013) no. 6, pp. 1260-1275.

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

We prove the independence of the strong uniformity principle from Church's thesis with choice in intuitionistic set theory with the axiom of extensionality extended by Markov's principle and the double complement for sets.
Keywords: intuitionistic logic, set theory, universe of sets, recursive realizability, Church's thesis, uniformity principle, extensionality function of a set. 
@article{IM2_2013_77_6_a6,
     author = {V. Kh. Khakhanyan},
     title = {Independence of the uniformity principle from {Church's} thesis in intuitionistic set theory},
     journal = {Izvestiya. Mathematics },
     pages = {1260--1275},
     publisher = {mathdoc},
     volume = {77},
     number = {6},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2013_77_6_a6/}
}
TY  - JOUR
AU  - V. Kh. Khakhanyan
TI  - Independence of the uniformity principle from Church's thesis in intuitionistic set theory
JO  - Izvestiya. Mathematics 
PY  - 2013
SP  - 1260
EP  - 1275
VL  - 77
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2013_77_6_a6/
LA  - en
ID  - IM2_2013_77_6_a6
ER  - 
%0 Journal Article
%A V. Kh. Khakhanyan
%T Independence of the uniformity principle from Church's thesis in intuitionistic set theory
%J Izvestiya. Mathematics 
%D 2013
%P 1260-1275
%V 77
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2013_77_6_a6/
%G en
%F IM2_2013_77_6_a6
V. Kh. Khakhanyan. Independence of the uniformity principle from Church's thesis in intuitionistic set theory. Izvestiya. Mathematics , Tome 77 (2013) no. 6, pp. 1260-1275. http://geodesic.mathdoc.fr/item/IM2_2013_77_6_a6/

[1] A. G. Dragalin, Mathematical intuitionism. Introduction to proof theory, Transl. Math. Monogr., 67, Amer. Math. Soc., Providence, RI, 1988 | MR | MR | Zbl | Zbl

[2] V. Kh. Khakhanyan, “Nondeducibility of the uniformization principles from Church's thesis in intuitionistic set theory”, Math. Notes, 43:5 (1988), 394–398 | DOI | MR | Zbl | Zbl

[3] A. S. Troelstra, “Notes on intuitionistic second order arithmetic”, Cambridge Summer School in Mathematical Logic (Cambridge, 1971), Lecture Notes in Math., 337, Springer-Verlag, Berlin, 1973, 171–205 | DOI | MR | Zbl

[4] V. Kh. Khakhanyan, “Teoriya mnozhestv i tezis Chercha”, Issledovaniya po neklassicheskim logikam i formalnym sistemam, Nauka, M., 1983, 198–208 | MR

[5] V. Kh. Khakhanyan, “Neprotivorechivost intuitsionistskoi teorii mnozhestv s printsipami Chercha i uniformizatsii”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1980, no. 5, 3–7 | MR | Zbl

[6] G. F. Shvarts, “Nekotorye primeneniya metoda rekursivnoi realizuemosti k intuitsionistskoi teorii tipov”, Voprosy kibernetiki. Neklassicheskie logiki i ikh primenenie, Nauchnyi sovet po kompleksnoi probleme “kibernetika”, M., 1982, 37–54

[7] V. Kh. Khakhanyan, “Nezavisimost silnogo printsipa uniformizatsii ot tezisa Chercha v polnoi teorii mnozhestv”, Nauchnye matematicheskie chteniya pamyati M. Ya. Suslina, Tez. dokladov (Saratov, 1989), SGPI, Saratov, 1989, 91

[8] S. C. Kleene, Introduction to metamathematics, North-Holland, Amsterdam, 1952 | MR | Zbl

[9] V. Kh. Khakhanyan, “The comparative strength of variants of Church's thesis at the level of set theory”, Soviet Math. Dokl., 21:3 (1980), 894–898 | MR | Zbl

[10] V. H. Hahanyan, “The consistency of some intuitionistic and constructive principles with a set theory”, Studia Logica, 40:3 (1981), 237–248 | DOI | MR | Zbl

[11] V. Kh. Khakhanyan, “The consistency of intuitionistic set theory with formal mathematical analysis”, Soviet Math. Dokl., 22 (1980), 46–50 | MR | Zbl