Geodesic
Solvability of equations and the continuum hypothesis
Dalʹnevostočnyj matematičeskij žurnal, Tome 4 (2003) no. 2, pp. 162-166.

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

Up to now the questions about the existence of the solutions for some important systems of equations of the mathematical physics are open. The purpose of this paper is to put forward the conjecture that the solvability of these equations could be depended of the axioms of the set theory. We build the system of linear equations whose solvability is equivalent to the continuum hypothesis. 
@article{DVMG_2003_4_2_a1,
     author = {A. A. Khusainov},
     title = {Solvability of equations and the continuum hypothesis},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {162--166},
     publisher = {mathdoc},
     volume = {4},
     number = {2},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2003_4_2_a1/}
}
TY  - JOUR
AU  - A. A. Khusainov
TI  - Solvability of equations and the continuum hypothesis
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2003
SP  - 162
EP  - 166
VL  - 4
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DVMG_2003_4_2_a1/
LA  - ru
ID  - DVMG_2003_4_2_a1
ER  - 
%0 Journal Article
%A A. A. Khusainov
%T Solvability of equations and the continuum hypothesis
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2003
%P 162-166
%V 4
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DVMG_2003_4_2_a1/
%G ru
%F DVMG_2003_4_2_a1
A. A. Khusainov. Solvability of equations and the continuum hypothesis. Dalʹnevostočnyj matematičeskij žurnal, Tome 4 (2003) no. 2, pp. 162-166. http://geodesic.mathdoc.fr/item/DVMG_2003_4_2_a1/

[1] B. Mitchell, “Rings with several objects”, Adv. math., 8 (1972), 1–161 | DOI | MR | Zbl

[2] B. Mitchell, “The cohomological dimension of a direct set”, Canad. J. Math., 25:2 (1973), 233–238 | MR | Zbl

[3] S. Marde$\check s$i$\acute c$, V. Prasolov, “Strong homology is not additive”, Trans. Amer. Math. Soc., 307:2 (1988), 725–744 | DOI | MR | Zbl

[4] A. Dow, P. Simon, J. E. Vaughan, “Strong homology and the proper forcing axiom”, Proc. Amer. Math. Soc., 106:3 (1989), 821–828 | MR | Zbl

[5] A. A. Khusainov, “Razmernost Khokhshilda-Mitchela lineino uporyadochennykh mnozhestv i gipoteza kontinuuma”, Sib. mat. zhurn., 35:5 (1994), 1171–1184 | MR | Zbl

[6] E. G. Sklyarenko, “Nekotorye primeneniya funktora lim$^1$”, Mat. sb., 123:3 (1984), 369–390 | MR

[7] A. A. Khusainov, “Ne lim-atsiklichnye summy kopii”, Sib. mat. zhurn., 37:2 (1996), 464–474 | MR | Zbl