Closure properties of countable non-standard integers
Completion closed algebras and models of Peano arithmetic
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,...
Conservative extensions of models of arithmetic.
Constructibility and shiftings of view
Constructions of classes by transfinite induction in AST
Cuts of real classes