Displaying similar documents to “Construction of the class FN”

Complexity of the axioms of the alternative set theory

Antonín Sochor (1993)

Commentationes Mathematicae Universitatis Carolinae

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If is a complete theory stronger than Fin such that axiom of extensionality for classes + + ( ∃ X ) Φ i is consistent for 1 ≤ i ≤ k (each alone), where Φ i are normal formulae then we show + ( ∃ X ) Φ 1 + ⋯ + ( ∃ X ) Φ k + scheme of choice is consistent. As a consequence we get: there is no proper Δ 1 -formula in + scheme of choice. Moreover the complexity of the axioms of 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...