Geodesic
On the structure of the Boolean-valued universe
Vladikavkazskij matematičeskij žurnal, Tome 20 (2018) no. 2, pp. 38-48 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The logical machinery is clarified which justifies declaration of hypotheses. In particular, attention is paid to hypotheses and conclusions constituted by infinitely many formulas. The formal definitions are presented for a Boolean-valued algebraic system and model of a theory, for the system of terms of the Boolean-valued truth value of formulas, for ascent and mixing. Logical interrelations are described between the ascent, mixing, and maximum principles. It is shown that every mixing with arbitrary weights can be transformed into a mixing with constant weight. The notion of restriction of an element of a Boolean-valued algebraic system is introduced and studied. It is proven that every Boolean-valued model of Set theory which meets the ascent principle has some multilevel structure analogous to von Neumann's cumulative hierarchy. 
@article{VMJ_2018_20_2_a4,
     author = {A. E. Gutman},
     title = {On the structure of the {Boolean-valued} universe},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {38--48},
     year = {2018},
     volume = {20},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2018_20_2_a4/}
}
TY  - JOUR
AU  - A. E. Gutman
TI  - On the structure of the Boolean-valued universe
JO  - Vladikavkazskij matematičeskij žurnal
PY  - 2018
SP  - 38
EP  - 48
VL  - 20
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VMJ_2018_20_2_a4/
LA  - ru
ID  - VMJ_2018_20_2_a4
ER  - 
%0 Journal Article
%A A. E. Gutman
%T On the structure of the Boolean-valued universe
%J Vladikavkazskij matematičeskij žurnal
%D 2018
%P 38-48
%V 20
%N 2
%U http://geodesic.mathdoc.fr/item/VMJ_2018_20_2_a4/
%G ru
%F VMJ_2018_20_2_a4
A. E. Gutman. On the structure of the Boolean-valued universe. Vladikavkazskij matematičeskij žurnal, Tome 20 (2018) no. 2, pp. 38-48. http://geodesic.mathdoc.fr/item/VMJ_2018_20_2_a4/

[1] Gutman A. E., “An example of using $\Delta_1$ terms in Boolean valued analysis”, Vladikavkaz Math. J., 14:1 (2012), 47–63 (in Russian) | DOI | MR | Zbl

[2] Gutman A. E., Losenkov G. A., “Function representation of the Boolean-valued universe”, Siberian Adv. Math., 8:1 (1998), 99–120 | MR | MR | Zbl

[3] Kusraev A. G., Kutateladze S. S., Introduction to Boolean Valued Analysis, Nauka, M., 2005, 529 pp. | MR

[4] Solovay R. M., Tennenbaum S., “Iterated Cohen extensions and Souslin's problem”, Annals of Math., 94:2 (1971), 201–245 | DOI | MR | Zbl