The models of a non-multidimensional -stable theory
The monadic second-order logic of graphs III : tree-decompositions, minors and complexity issues
The -propositional calculus
T. Almada and J. Vaz de Carvalho (2001) stated the problem to investigate if these Łukasiewicz algebras are algebras of some logic system. In this article an affirmative answer is given and the -propositional calculus, denoted by , is introduced in terms of the binary connectives (implication), (standard implication), (conjunction), (disjunction) and the unary ones (negation) and , (generalized Moisil operators). It is proved that belongs to the class of standard systems of implicative...
The Neg.-propositional Calculus
The nonabsolute boundedness model of the theory of semisets
The non-axiomatizability of the observational predicate calculus (generalized Trachtenbrot's theorems)
The nonexistence of robust codes for subsets of ω₁
Several results are presented concerning the existence or nonexistence, for a subset S of ω₁, of a real r which works as a robust code for S with respect to a given sequence of pairwise disjoint stationary subsets of ω₁, where “robustness” of r as a code may either mean that whenever each is equal to modulo nonstationary changes, or may have the weaker meaning that for every club C ⊆ ω₁. Variants of the above theme are also considered which result when the requirement that S gets exactly...
The non-existence of well-orderings of the Cantor set
The notion of an elementary subsystem for a Boolean-valued relational system
The notions of w-net and Y-compact space viewed under infinitesimal microscope.
The null ideal restricted to some non-null set may be ℵ₁-saturated
Our main result is that possibly some non-null set of reals cannot be divided into uncountably many non-null sets. We also deal with a non-null set of real, the graph of any function from which is null, and deal with our iterations somewhat more generally.
The Number Of Antichains Of Finite Power Sets
The number of antichains of finite power sets.
The number of automorphisms of models of -categorical theories
The number of countable generic models for finite forcing
The number of countable isomorphism types of complete extensions of the theory of Boolean algebras
There is a conjecture of Vaught [17] which states: Without The Generalized Continuum Hypothesis one can prove the existence of a complete theory with exactly nonisomorphic, denumerable models. In this paper we show that there is no such theory in the class of complete extensions of the theory of Boolean algebras. More precisely, any complete extension of the theory of Boolean algebras has either 1 or nonisomorphic, countable models. Thus we answer this conjecture in the negative for any complete...
The number of countable models of a theory of one unary function
The number of -equivalent nonisomorphic models for κ weakly compact
For a cardinal κ and a model M of cardinality κ let No(M) denote the number of nonisomorphic models of cardinality κ which are -equivalent to M. We prove that for κ a weakly compact cardinal, the question of the possible values of No(M) for models M of cardinality κ is equivalent to the question of the possible numbers of equivalence classes of equivalence relations which are Σ¹₁-definable over . By [SV] it is possible to have a generic extension where the possible numbers of equivalence classes...
The observational predicate calculus and complexity of computations (Preliminary communication)
The operator gap theorem in ...-recursion theory.