摘要:

AbstractConcepts ofL1space, integrable functions and integrals are formalized in weak subsystems of second order arithmetic. They are discussed especially in relation with the combinatorial principle WWKL (weak‐weak König's lemma and arithmetical comprehension. Lebesgue dominated convergence theorem is proved to be equivalent to arithmetical comprehension. A weak version of Lebesgue monotone convergence theorem is proved to be equivalent to weak‐weak König's lemma.Mathematics Subject Classification:

ISSN:0942-5616    

DOI:10.1002/malq.19940400102

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1994

数据来源: WILEY

摘要:

AbstractWe characterize preservation of superstability and ω‐stability for finite extensions of abelian groups and reduce the general case to the case ofp‐groups. In particular we study finite extensions of divisible abelian groups. We prove that superstable abelian‐by‐finite groups have only finitely many conjugacy classes of Sylowp‐subgroups.Mathematics Subject Classification:03

ISSN:0942-5616    

DOI:10.1002/malq.19940400103

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1994

数据来源: WILEY

摘要:

AbstractIt is shown by Parsons [2] that the first‐order fragment of Frege's (inconsistent) logical system in theGrundgesetze der Arithmeticis consistent. In this note we formulate and prove a stronger version of this result for arbitrary first‐order theories. We also show that a natural attempt to further strengthen our result runs afoul of Tarski's theorem on the undefinability of truth.Mathematics Subject Classification:03

ISSN:0942-5616    

DOI:10.1002/malq.19940400104

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1994

数据来源: WILEY

摘要:

AbstractIt is known (see Rapp [9]) that elementary geometry with the additional quantifier “there exist uncountably many” is decidable. We show that this decidability helps in solving the following problem from combinatorial geometry: does there exist an uncountable family of pairwise non‐congruent tetrahedra that aren‐equidecomposable with a cube?Mathematics Subject Classification:03B25, 03C80, 51M04, 52B05

ISSN:0942-5616    

DOI:10.1002/malq.19940400105

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1994

数据来源: WILEY

摘要:

AbstractWe examine, from a constructive perspective, the relation between the complements ofS, T, andS∩TinX, whereXis either a metric space or a normed linear space. The fundamental question addressed is: Ifxis distinct from each element ofS∩T, ifsϵS, and iftϵT, isxdistinct fromsor fromt? Although the classical answer to this question is trivially affirmative, constructive answers involve Markov's principle and the completeness of metric spaces.Mathematics Subject Classification:03F65,

ISSN:0942-5616    

DOI:10.1002/malq.19940400106

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1994

数据来源: WILEY

摘要:

AbstractA translation of formulas in a languageL1to formulas in a languageL2is a mapping which preserves the parameters and commutes with the substitution prefix, the propositional connectives and the quantifiers. Every translation generates a corresponding transformation of theories inL1to theories inL2. We formulate the equiconsistency problem for such transformations and propose a variant of its solution. First, for a transformationFwe find the least theoryA(F) inL1such that its inclusion in a theoryT(inL1) guarantees equiconsistency ofFandF(T), then we propose axiomatizations ofA(F) for someF's.Mathematics Subject Classification:03B10, 03B15, 03F25.

ISSN:0942-5616    

DOI:10.1002/malq.19940400107

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1994

数据来源: WILEY

摘要:

AbstractProceeding in the theory with extensionality, comprehension for classes, existence of the empty set and the assumption the addition of one element to a set makes again a set (others usual set‐theoretical operations are not required) we show a week assumption which guarantees existence of a saturated elementary extension (with absolute ϵ) of the system of hereditarily finite sets.Mathematics Subject Classification:03C62, 03C50, 03E

ISSN:0942-5616    

DOI:10.1002/malq.19940400108

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1994

数据来源: WILEY

摘要:

AbstractIn this paper we obtain a finite Hilbert‐style axiomatization of the implicationless fragment of the intuitionistic propositional calculus. As a consequence we obtain finite axiomatizations of all structural closure operators on the algebra of {–}‐formulas containing this fragment.Mathematics Subject Classification:03B20, 03B22,

ISSN:0942-5616    

DOI:10.1002/malq.19940400109

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1994

数据来源: WILEY

摘要:

AbstractIn conventional generalization of the main results of classical measure theory to Stone algebra valued measures, the values that measures and functions can take are Booleanized, while the classical notion of a σ‐field is retained. The main purpose of this paper is to show by abundace of illustrations that if we agree to Booleanize the notion of a σ‐field as well, then all the glorious legacy of classical measure theory is preserved completely.Mathematics Subject Classification:03C90,

ISSN:0942-5616    

DOI:10.1002/malq.19940400110

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1994

数据来源: WILEY

摘要:

AbstractIn this paper we provide a quantifier‐free constructive axiomatization for Euclidean planes in a first‐order language with only ternary operation symbols and three constant symbols (to be interpreted as ‘points’). We also determine the algorithmic theories of some ‘naturally occurring’ plane geometries.Mathematics Subject Classification:03F65, 51M05, 5

ISSN:0942-5616    

DOI:10.1002/malq.19940400111

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1994

数据来源: WILEY