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DOI: 10.23671/VNC.2018.2.14718 On the Structure of the BooleanValued Universe
Gutman, A. E.
Vladikavkaz Mathematical Journal 2018. Vol. 20. Issue 2.
Abstract:
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 Booleanvalued algebraic system and model of a theory, for the system of terms of the Booleanvalued 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 Booleanvalued algebraic system is introduced and studied. It is proven that every Booleanvalued model of Set theory which meets the ascent principle has some multilevel structure analogous to von Neumann's cumulative hierarchy.
Keywords: set theory, Booleanvalued model, universe, cumulative hierarchy
Language: Russian
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For citation: Gutman A. E. On the Structure of the BooleanValued Universe.
Vladikavkazskij matematicheskij zhurnal [Vladikavkaz Math. J.], vol.
20, no. 2, pp. 3848.
DOI 10.23671/VNC.2018.2.14718 ← Contents of issue 
 

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