FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1999, VOLUME 5, NUMBER 2, PAGES 417-435

**A two-sorted theory of classes and sets, admitting sets of
propositional formulas**

V. K. Zakharov

A. V. Mikhalev

Abstract

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```
The crisis arisen in the naive set theory in the beginning
of the 20th century brought to the origin of such strict
axiomatic theories as the \emph{theory of sets in
Zermelo--Fraenkel's axiomatics} (ZF) and
the \emph{theory of classes and sets in Neumann--Bernays--G\"odel's axiomatics} (NBG). However, in
the same time as the naive set theory admitted
considering sets of arbitrary objects, such
a natural notion as a \emph{set of propositional formulas}
became inadmissible in ZF and NBG. In connection with this
circumstance some methods of associated admission were
developed, the most known of which is the \emph{method of
G\"odel's enumeration}.
```

This paper is devoted to a solution of the \emph{full
rights admission problem}. An axiomatics of
the \emph{two-sorted theory of classes and sets} is
exposed in it, which allows to consider sets of
propositional formulas equally with sets of object
elements.

All articles are
published in Russian.

Location: http://mech.math.msu.su/~fpm/eng/99/992/99205t.htm

Last modified: July 6, 1999