Complexity of the axioms of the alternative set theory
نویسنده
چکیده
If T is a complete theory stronger than ZFFin such that axiom of extensionality for classes + T + (9X) i is consistent for 1 i k (each alone), where i are normal formulae then we showAST + (9X) 1+ +(9X) k + scheme of choice is consistent. As a consequence we get: there is no proper 1-formula inAST + scheme of choice. Moreover the complexity of the axioms of AST is studied, e.g. we show axiom of extensionality is 1-formula, but not 1-formula and furthermore prolongation axiom, axioms of choice and cardinalities are 2-formulae, but not 1-formulae in AST without the axiom in question.
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