On interpolation when function symbols are present.
On interpretability in set theories
On interpretability in set theories. II.
On interpretability in theories containing arithmetic
On interpretability in theories containing arithmetic. II.
On intersections of sets of positive Lebesgue measure
On Intuitionistic Sentential Connectives I.
On invariant CCC -ideals
On invariant, dual invariant and absolute formulas [Book]
On invariants for measure preserving transformations
The classification problem for measure preserving transformations is strictly more complicated than that of graph isomorphism.
On isomorphism classes of spaces
We provide a complete isomorphic classification of the Banach spaces of continuous functions on the compact spaces , the topological sums of Cantor cubes , with smaller than the first sequential cardinal, and intervals of ordinal numbers [0,α]. In particular, we prove that it is relatively consistent with ZFC that the only isomorphism classes of spaces with ≥ ℵ₀ and α ≥ ω₁ are the trivial ones. This result leads to some elementary questions on large cardinals.
On isomorphisms between -ideals on
On isomorphisms of inner product spaces
On iterated forcing for successors of regular cardinals
We investigate the problem of when ≤λ-support iterations of < λ-complete notions of forcing preserve λ⁺. We isolate a property- properness over diamonds-that implies λ⁺ is preserved and show that this property is preserved by λ-support iterations. Our condition is a relative of that presented by Rosłanowski and Shelah in [2]; it is not clear if the two conditions are equivalent. We close with an application of our technology by presenting a consistency result on uniformizing colorings of ladder...
On joint distribution in quantum logics. I. Compatible observables
The notion of a joint distribution in -finite measures of observables of a quantum logic defined on some system of -independent Boolean sub--algebras of a Boolean -algebra is studied. In the present first part of the paper the author studies a joint distribution of compatible observables. It is shown that it may exists, although a joint obsevable of compatible observables need not exist.
On joint distribution in quantum logics. II. Noncompatible observables
This paper i a continuation of the first part under the same title. The author studies a joint distribution in -finite measures for noncompatible observables of a quantum logic defined on some system of -independent Boolean sub--algebras of a Boolean -algebra. We present some necessary and sufficient conditions fot the existence of a joint distribution. In particular, it is shown that an arbitrary system of obsevables has a joint distribution in a measure iff it may be embedded into a system...
On Kalmar's consistency proof and a generalization of the notion of ...-consistency.
On knowledge games.
We give a formalization of the ?knowledge games? which allows to study their decidability and convergence as a problem of mathematics. Our approach is based on a metalemma analogous to those of Von Neumann and Morgenstern at the beginning of Game Theory. We are led to definitions which characterize the knowledge games as objects is standard set theory. We then study rigorously the most classical knowledge games and, although we also prove that the ?common knowledge? in these games may be incomputable,...
On Krull's intersection theorem of fuzzy ideals.
On L 1 Space Formed by Complex-Valued Partial Functions
In this article, we formalized L1 space formed by complexvalued partial functions [11], [15]. The real-valued case was formalized in [22] and this article is its generalization.