Geodesic
Function Representation of the~Boolean-Valued Universe
Matematičeskie trudy, Tome 1 (1998) no. 1, pp. 54-77

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

For an abstract Boolean-valued system, a function analog is proposed that is a model whose elements are functions and the basic logical operations are calculated “pointwise”. The new notion of continuous polyverse is introduced and studied which is a continuous bundle of models of set theory. It is shown that the class of continuous sections of a continuous polyverse is a Boolean-valued system satisfying all basic principles of Boolean-valued analysis and, conversely, every Boolean-valued algebraic system can be represented as the class of sections of a suitable continuous polyverse. 
@article{MT_1998_1_1_a2,
     author = {A. E. Gutman and G. A. Losenkov},
     title = {Function {Representation} of {the~Boolean-Valued} {Universe}},
     journal = {Matemati\v{c}eskie trudy},
     pages = {54--77},
     publisher = {mathdoc},
     volume = {1},
     number = {1},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_1998_1_1_a2/}
}
TY  - JOUR
AU  - A. E. Gutman
AU  - G. A. Losenkov
TI  - Function Representation of the~Boolean-Valued Universe
JO  - Matematičeskie trudy
PY  - 1998
SP  - 54
EP  - 77
VL  - 1
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MT_1998_1_1_a2/
LA  - ru
ID  - MT_1998_1_1_a2
ER  - 
%0 Journal Article
%A A. E. Gutman
%A G. A. Losenkov
%T Function Representation of the~Boolean-Valued Universe
%J Matematičeskie trudy
%D 1998
%P 54-77
%V 1
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MT_1998_1_1_a2/
%G ru
%F MT_1998_1_1_a2
A. E. Gutman; G. A. Losenkov. Function Representation of the~Boolean-Valued Universe. Matematičeskie trudy, Tome 1 (1998) no. 1, pp. 54-77. http://geodesic.mathdoc.fr/item/MT_1998_1_1_a2/