## A preliminary investigation of the infinitely-many-valued predicate calculus |

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### Contents

Definitions | 5 |

Structure of the Models | 22 |

Axiomatic Descriptions The Propositional Calculus | 34 |

2 other sections not shown

### Common terms and phrases

aA3r apply Lemma axiomatization basis elements class type clearly completes the proof congruence relations constant-valued function construction continuous with slope corresponding defining model elements of 3A elements of WFFm equivalence classes equivalence relation factor algebra finite number finitely-many-valued system functional monadic Chang functional representation funotions given Hahn's Halmos Hence homomorphism hypothesis ideal of 3A induction infinitely-many-valued propositional calculus integer interpretation intuitive isomorphic linear linearly ordered abelian linearly ordered Chang Linearly Ordered Groups logical m-valued many-valued mapping maximal ideals monadic Chang algebra monadic ideals monadic predicate calculus monadio non-zero element oaloulus obtained ordered abelian groups ordered Chang algebra pointwise definition prime ideals properties provable rational numbers real numbers satisfies sequence subalgebra subdirect product subset supremum operator Theorem theory of linearly total depth two-valued uniformly continuous valid value set well-formed formulas well-ordering WFFp WFFs whioh Xukasiewicz