1. |
Lebesgue Convergence Theorems and Reverse Mathematics |
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Mathematical Logic Quarterly,
Volume 40,
Issue 1,
1994,
Page 1-13
Xiaokang Yu,
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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
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2. |
On Preservation of Stability for Finite Extensions of Abelian Groups |
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Mathematical Logic Quarterly,
Volume 40,
Issue 1,
1994,
Page 14-26
Frieder Haug,
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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
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3. |
Fregean Extensions of First‐Order Theories |
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Mathematical Logic Quarterly,
Volume 40,
Issue 1,
1994,
Page 27-30
John L. Bell,
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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
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4. |
An Application of Logic to Combinatorial Geometry: How Many Tetrahedra are Equidecomposable with a Cube? |
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Mathematical Logic Quarterly,
Volume 40,
Issue 1,
1994,
Page 31-34
Vladik Kreinovich,
Olga Kosheleva,
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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
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5. |
Complements of Intersections in Constructive Mathematics |
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Mathematical Logic Quarterly,
Volume 40,
Issue 1,
1994,
Page 35-43
Douglas S. Bridges,
Hajime Ishihara,
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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
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6. |
Translations of Logical Formulas and the Equiconsistency Problem |
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Mathematical Logic Quarterly,
Volume 40,
Issue 1,
1994,
Page 44-50
Andrei A. Kuzichev,
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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
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7. |
Choices of Convenient Sets |
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Mathematical Logic Quarterly,
Volume 40,
Issue 1,
1994,
Page 51-60
Antonín Sochor,
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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
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8. |
A Finite Hilbert‐Style Axiomatization of the Implication‐Less Fragment of the Intuitionistic Propositional Calculus |
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Mathematical Logic Quarterly,
Volume 40,
Issue 1,
1994,
Page 61-68
Jordi Rebagliato,
Ventura Verdú,
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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
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9. |
Boolean Valued and Stone Algebra Valued Measure Theories |
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Mathematical Logic Quarterly,
Volume 40,
Issue 1,
1994,
Page 69-75
Hirokazu Nishimura,
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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
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10. |
Ternary Operations as Primitive Notions for Constructive Plane Geometry IV |
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Mathematical Logic Quarterly,
Volume 40,
Issue 1,
1994,
Page 76-86
Victor Pambuccian,
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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
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