Some generalizations to two systems of set theory based on combinatory logic.
Some remarks on bicommutability
Some remarks on revealness
Some remarks to the axiom of prolongation
Starkes und überstarkes Auswahlaxiom.
Sur les arbres logiques de M. Krasner
The axiom of reflection
The consistency of the measurability of projective semisets
The interpreted type-free modal calculus
The interpreted type-free modal calculus
The interpreted type-free modal calculus . II
The lattice of indiscernibility equivalences
The nonabsolute boundedness model of the theory of semisets
The quantifier complexity of NF.
Ultrafilters and endomorphic universes
Ultrafilters of sets
Uncountable cardinals have the same monadic ∀₁¹ positive theory over large sets
We show that uncountable cardinals are indistinguishable by sentences of the monadic second-order language of order of the form (∀X)ϕ(X) and (∃X)ϕ(X), for ϕ positive in X and containing no set-quantifiers, when the set variables range over large (= cofinal) subsets of the cardinals. This strengthens the result of Doner-Mostowski-Tarski [3] that (κ,∈), (λ,∈) are elementarily equivalent when κ, λ are uncountable. It follows that we can consistently postulate that the structures , are indistinguishable...
Utility theory in the alternative set theory
Valuations of lines
We enlarge the problem of valuations of triads on so called lines. A line in an -structure (it means that is a semigroup and is an automorphism or an antiautomorphism on such that ) is, generally, a sequence , , (where is the class of finite integers) of substructures of such that holds for each . We denote this line as and we say that a mapping is a valuation of the line in a line if it is, for each , a valuation of the triad in . Some theorems on an existence of...
Valuations of structures