摘要:

AbstractWe give a polynomial time controlled version of a theorem of M. Hall: every real number can be written as the sum of two irrational numbers whose developments into a continued fraction contain only 1, 2, 3 or 4.Mathematics Subject Classification:03D15, 03F60, 11A55, 68Q25.

ISSN:0942-5616    

DOI:10.1002/malq.19960420112

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1996

数据来源: WILEY

摘要:

AbstractWe shall describe the set of strongly meet irreducible logics in the lattice ϵLin.tof normal tense logics (in the bimodal propositional language) of weak orderings. Based on this description it is shown that all logics in ϵLin.tare independently axiomatizable. Then the description is used in order to investigate tense logics with respect to decidability, finite axiomatizability, axiomatization problems and completeness with respect to Kripke semantics. The main tool for the investigation is a translation of bimodal formulas into a language talking about partitions of general frames into intervals so that relative to both Kripke frames and descriptive frames the expressive power of both languages coincides.Mathematics Subject Classification:03B45, 03B2

ISSN:0942-5616    

DOI:10.1002/malq.19960420113

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1996

数据来源: WILEY

摘要:

AbstractWe show that for every uncountable regular κ and every κ‐complete Boolean algebraBof density ≤ κ there is a filterF⊆Bsuch that the number of partitions of length

ISSN:0942-5616    

DOI:10.1002/malq.19960420114

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1996

数据来源: WILEY

摘要:

AbstractThis paper articulates the structure of a two species of weakly aggregative necessity in a common idiom, neighbourhood semantics, using the notion of ak‐filter of propositions. Ak‐filter on a non‐empty setIis a collection of subsets ofIwhich (i) containsI, (ii) is closed under supersets onI, and (iii) contains ∪{Xi≤Xj: 0 ≤i

ISSN:0942-5616    

DOI:10.1002/malq.19960420115

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1996

数据来源: WILEY

摘要:

AbstractWe prove that there exists a nonzero recursively enumerable Turing degree possessing a strong minimal cover.Mathematics Subject Classification: 03D30.

ISSN:0942-5616    

DOI:10.1002/malq.19960420116

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1996

数据来源: WILEY

摘要:

AbstractWe develop cut‐free calculi of sequents for normal modal logics by using treesequents, which are trees of sequences of formulas. We introduce modal operators corresponding to the ways we move formulas along the branches of such trees, only considering fixed distance movements. Finally, we exhibit syntactic cut‐elimination theorems for all the main normal modal logics.Mathematics Subject Classification: 03B45, 03

ISSN:0942-5616    

DOI:10.1002/malq.19960420117

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1996

数据来源: WILEY

摘要:

AbstractAssuming Con(AD), a model in which there are unboundedly many regular cardinals below Θ and in which the only regular cardinals below Θ are limit cardinals was previously constructed. Using a large cardinal hypothesis far beyond Con(AD), we construct in this paper a model in which there is a proper class of regular cardinals and in which the only regular cardinals in the universe are limit cardinals.Mathematics Subject Classification: 03E55, 03E6

ISSN:0942-5616    

DOI:10.1002/malq.19960420118

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1996

数据来源: WILEY

摘要:

AbstractA polymodal lattice is a distributive lattice carrying ann‐place operator preserving top elements and certain finite meets. After exploring some of the basic properties of such structures, we investigate their freely generated instances and apply the results to the corresponding logical systems — polymodal logics — which constitute natural generalizations of the usual systems of modal logic familiar from the literature. We conclude by formulating an extension of Kripke semantics to classical polymodal logic and proving soundness and completeness theorems.Mathematics Subject Classification: 03G10, 06D99,

ISSN:0942-5616    

DOI:10.1002/malq.19960420119

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1996

数据来源: WILEY

摘要:

AbstractIn many‐valued logic the decision of functional completeness is a basic and important problem, and the thorough solution to this problem depends on determining all maximal closed sets in the set of many‐valued logic functions. It includes three famous problems, i.e., to determine all maximal closed sets in the set of the total, of the partial and of the unary many‐valued logic functions, respectively. The first two problems have been completely solved ([1], [2], [8]), and the solution to the third problem boils down to determining all maximal subgroups in thek‐degree symmetric groupSk, which is an open problem in the finite group theory. In this paper, all maximal closed sets in the set of unaryp‐valued logic functions are determined, wherepis a prime.Mathematics Subject Classification: 03B

ISSN:0942-5616    

DOI:10.1002/malq.19960420120

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1996

数据来源: WILEY

摘要:

AbstractR. Shore proved that every recursively enumerable (r. e.) set can be split into two (disjoint) nowhere simple sets. Splitting theorems play an important role in recursion theory since they provide information about the lattice ϵ of all r. e. sets. Nowhere simple sets were further studied by D. Miller and J. Remmel, and we generalize some of their results. We characterize r. e. sets which can be split into two (non) effectively nowhere simple sets, and r. e. sets which can be split into two r. e. non‐nowhere simple sets. We show that every r. e. set is either the disjoint union of two effectively nowhere simple sets or two noneffectively nowhere simple sets. We characterize r. e. sets whose every nontrivial splitting is into nowhere simple sets, and r. e. sets whose every nontrivial splitting is into effectively nowhere simple sets. R. Shore proved that for every effectively nowhere simple setA, the latticeL* (A) is effectively isomorphic to ϵ*, and that there is a nowhere simple setAsuch thatL*(A) is not effectively isomorphic to ϵ*. We prove that every nonzero r. e. Turing degree contains a noneffectively nowhere simple setAwith the latticeL*(A) effectively isomorphic to ϵ*.Mathematics Subject Classification: 03D25,

ISSN:0942-5616    

DOI:10.1002/malq.19960420121

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1996

数据来源: WILEY