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Complexity of the axioms of the alternative set theory

Antonín Sochor (1993)

Commentationes Mathematicae Universitatis Carolinae

If T is a complete theory stronger than ZF Fin such that axiom of extensionality for classes + T + ( X ) Φ i is consistent for 1 i k (each alone), where Φ i are normal formulae then we show AST + ( X ) Φ 1 + + ( X ) Φ k + scheme of choice is consistent. As a consequence we get: there is no proper Δ 1 -formula in AST + scheme of choice. Moreover the complexity of the axioms of AST is studied, e.gẇe show axiom of extensionality is Π 1 -formula, but not Σ 1 -formula and furthermore prolongation axiom, axioms of choice and cardinalities are Π 2 -formulae,...

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