In the first paper of this series it was shown that any unquantified formula p in the collection
MLSSF (multilevel syllogistic extended with the singleton operator and the predicate Finite) …

The class of unquantified formulae of set theory involving Boolean operators, the powerset
and singleton operators, and the equality and membership predicates is shown to have a …

We report on an investigation aimed at identifying small fragments of set theory (typically,
sublanguages of Multi-Level Syllogistic) endowed with polynomial-time satisfiability decision …

The Logically Simplest Form of the Infinity Axiom Page 1 PROCEEDINGS OF THE AMERICAN
MATHEMATICAL SOCIETY Volume 103, Number 1, May 1988 THE LOGICALLY SIMPLEST …

In [PP88] it is shown that GSdel's first incompleteness theorem can be proved in a
surprisingly weak theory of sets with formulae of very low complexity and as a consequence …

Let $\mathcal {L} _ {\mathcal {X}} $ be the language of first-order, decidable theory $\mathcal
{X} $. Consider the language, $\mathcal {L} _ {\mathcal {RQ}}(\mathcal {X}) $, that extends …

In this paper, which extends earlier work on decision proceures for various quantified and
unquantified restricted sublanguages of set theory (see [FOSSO, BFOS81, BF84, CFMS86]) …

Abstract Let\(\mathcal {L} _\mathcal {X}\) be the language of a first-order, decidable,
quantifier-free theory\(\mathcal {X}\). Consider the language,\(\mathcal {L} _\mathcal …

The problem of establishing whether there are sets satisfying a formula in the first order set
theoretic language ℒ︁ϵ based on=, ϵ, which involves only restricted quantifiers and has an …

Positive solutions to the decision problem for a class of quantified formulae of the first order
set theoretic language based on ϕ, ε,=, involving particular occurrences of restricted …