Axiomatizability of second order arithmetic with ω-rule
Basic equivalences in the alternative set theory
Biequivalence vector spaces in the alternative set theory
As a counterpart to classical topological vector spaces in the alternative set theory, biequivalence vector spaces (over the field of all rational numbers) are introduced and their basic properties are listed. A methodological consequence opening a new view towards the relationship between the algebraic and topological dual is quoted. The existence of various types of valuations on a biequivalence vector space inducing its biequivalence is proved. Normability is characterized in terms of total...
Biequivalences and topology in the alternative set theory
Borel classes in AST. Measurability, cuts and equivalence
Category theory based on combinatory logic.
Combinatoric properties of classes in AST
Complexity of the axioms of the alternative set theory
If T is a complete theory stronger than ZF such that axiom of extensionality for classes + T + is consistent for 1 (each alone), where are normal formulae then we show AST + + scheme of choice is consistent. As a consequence we get: there is no proper -formula in AST + scheme of choice. Moreover the complexity of the axioms of AST is studied, e.gẇe show axiom of extensionality is -formula, but not -formula and furthermore prolongation axiom, axioms of choice and cardinalities are -formulae,...
Constructibility and shiftings of view
Construction by transfinite induction
Construction of the class FN
Constructions of classes by transfinite induction in AST
Constructions of endomorphic universes and similarities
Correction to the paper “A notion of measure for classes in AST”
Correction to the paper: “Set-like equivalence and inner and outer cuts”
Correspondence between interval -equivalences and -functions
Countable inductive definitions in AST
Cuts of real classes
Definability degrees for classes in the alternative set theory
Degrees of dependence in the theory of semisets.