## Six Papers in Logic, Volume 135This book contains six papers in logic translated from the Russian. |

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### Contents

Solution of the Problem of Finite Axiomatizability for Theories that are Categorical in All Infinite Powers | 1 |

On a Solution of the Problem of Finite Axiomatizability for Theories Categorical in All Infinite Powers | 13 |

On Theories with a Basis | 19 |

Gentzen Systems of Postulates for Set Theory | 23 |

Arithmetically Complete Modal Theories | 39 |

On the Complexity of Shortest Disjunctive Normal Forms of Boolean Functions | 55 |

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### Common terms and phrases

A U B U Algebra algorithm arithmetical examples Assume atom axiom of choice axiom of extensionality axiomatizability for theories axioms B. I. Zil'ber basic sequents Boolean functions xn categorical theories chosen subcubes cl(X complete modal theories COROLLARY cut-rule deducible definable relative definition dimension fco equal exists extensions of arithmetic finite axiomatizability free occurrences free variable Gentzen H UJ implies index attached infinite powers integer Kripke models least natural number Lemma liberally stratified log log logn Math Mathematics Subject Classification modal logic nonlogical obtain polynomial Pr(r predicate primitive recursive primitive recursive function problem of finite proof of F proof of Lemma PROPOSITION provable in NTS proved quasiformula of NFS S-formulas sequent F sequent provable Solovay strict equivalence relation strongly minimal subcube 3i subcubes of dimension subset sufficiently large systems of postulates theorem type indices type theory UJ UJ vertices well-formed formula well-formed term ZFS+