Alternative set theory with elementary classes

Nando Prati

Displaying similar documents to “Alternative set theory with elementary classes”

On a weak Kelley-Morse theory of classes

Wiktor V. Marek, Antonín Sochor (1978)

Commentationes Mathematicae Universitatis Carolinae

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Metamathematics of the alternative set theory. I.

Antonín Sochor (1979)

Commentationes Mathematicae Universitatis Carolinae

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Internal and forcing models for the impredicative theory of classes

Rolando Chuaqui

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CONTENTSIntroduction............................................................................................................ 5I. Axiom system and elementary consequences........................................... 61. Axioms........................................................................................................................ 62. Definitions and elementary consequences........................................................ 9II. Principles of definitions by recursion..............................................................

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 + + $(\exists X) Φ_{i}$ is consistent for 1 $\leq i \leq k$ (each alone), where $Φ_{i}$ are normal formulae then we show + $(\exists X) Φ_{1} + \dots + (\exists X) Φ_{k}$ + 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...