摘要:

AbstractIn [2], Jockusch and Shore have introduced a new hierarchy of sets and operators called the REA hierarchy. In this note we prove analogues of the Friedberg Jump Theorem and the Sacks Jump Theorem for many REA operators. MSC: 03D25, 03D55.

ISSN:0942-5616    

DOI:10.1002/malq.19930390103

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1993

数据来源: WILEY

摘要:

AbstractIn this paper we study some statements similar to the Partition Principle and the Trichotomy. We prove some relationships between these statements, the Axiom of Choice, and the Generalized Continuum Hypothesis. We also prove some independence results. MSC: 03E25, 03E50, 04A25, 04A50.

ISSN:0942-5616    

DOI:10.1002/malq.19930390104

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1993

数据来源: WILEY

摘要:

AbstractBy creating an unbounded topological reduction theory for complex Hilbert spaces over Stonean spaces, we can give a category‐theoretic duality between Boolean valued analysis and topological reduction theory for complex Hilbert spaces. MSC: 03C90, 03E40, 06E15, 46M9

ISSN:0942-5616    

DOI:10.1002/malq.19930390105

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1993

数据来源: WILEY

摘要:

AbstractThis paper introduces the notion of cW10‐creative set, which strengthens that of semicreative set in a similar way as complete creativity strengthens creativity. Two results are proven, both of which imply that not all semicreative sets are cW10‐creative. First, it is shown that semicreative Dedekind cuts cannot be cW10‐creative; the existence of semicreative Dedekind cuts was shown by Soare. Secondly, it is shown that (i) ifA⊕B, the join ofAandB, is cW10‐creative, then eitherAorBis cW10‐creative, and (ii) the same is not true with ‘cW10‐creative’ replaced by ‘semicreative’. Moreover, setsA,Bwhich provide a counterexample for (ii) can be constructed within any given nonrecursive r.e. T‐d

ISSN:0942-5616    

DOI:10.1002/malq.19930390106

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1993

数据来源: WILEY

摘要:

AbstractIn ordinal analysis of impredicative theories so‐called collapsing functions are of central importance. Unfortunately, the definition procedure of these functions makes essential use of uncountable cardinals whereas the notation system that they call into being corresponds to a recursive ordinal. It has long been claimed that, instead, one should manage to develop such functions directly on the basis of admissible ordinals. This paper is meant to show how this can be done. Interpreting the collapsing functions as operating directly on admissible sets also renders a new and perspicuous approach to well‐ordering proofs possible. MSC: 03F15, 03

ISSN:0942-5616    

DOI:10.1002/malq.19930390107

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1993

数据来源: WILEY

摘要:

AbstractThe main result of this paper is a weak constructive version of the uniform continuity theorem for pointwise continuous, real‐valued functions on a convex subset of a normed linear space. Recursive examples are given to show that the hypotheses of this theorem are necessary. The remainder of the paper discusses conditions which ensure that a sequentially continuous function is continuous. MSC: 03F60, 26E40, 46S3

ISSN:0942-5616    

DOI:10.1002/malq.19930390108

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1993

数据来源: WILEY

摘要:

AbstractWe consider minimal ranks of extenders associated with Shelah cardinals by introducing witnessing numbers. Using these numbers we shall investigate effects of Shelah cardinals above themselves. MSC: 03E55.

ISSN:0942-5616    

DOI:10.1002/malq.19930390109

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1993

数据来源: WILEY

摘要:

AbstractIn transfinite arithmetic 2nis defined as the cardinality of the family ofallsubsets of some setvwith cardinalityn.However, in the arithmetic of recursive equivalence types (RETs) 2Nis defined as the RET of the family ofall finitesubsets of some setvof nonnegative integers with RETN.Supposevis a nonempty set.Sis aclass over v, ifSconsists of finite subsets ofvand hasvas its union. Such a class is anintersecting class(IC) overv, if every two members ofShave a nonempty intersection. An IC overvis called amaximal IC(MIC), if it is not properly included in any IC overv.It is known and readily proved that every MIC over a finite setvof cardinalityn≥ 1 has cardinality 2n‐1. In order to generalize this result we introduce the notion of an ω‐MIC overv.This is an effective analogue ot the notion of an MIC overvsuch that a class over afinitesetvis an ω‐MIC iff it is an MIC. We then prove that every ω‐MIC over anisolatedsetvof RETN≥ 1 has RET 2N‐1. This is a generalization, for while there only are χ0finite sets, there are ϰ isolated sets, wherecdenotes the cardinality of the continuum, namely all the finite sets and thecimmun

ISSN:0942-5616    

DOI:10.1002/malq.19930390110

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1993

数据来源: WILEY

摘要:

AbstractAdding higher types to set theory differs from adding inaccessible cardinals, in that higher type arguments apply to all sets rather than just ordinary ones. Levy's reflection axiom is justified, by considering the principle that we can pretend that the universe is a set, together with methods of Gaifman [8]. We reprove some results of Gaifman, and some facts about Levy's reflection axiom, including the fact that adding higher types yields no new theorems about sets. Some remarks on standard models are made. An obvious strengthening of Levy's axiom to higher types is considered, which implies the existence of indescribable cardinals. Other remarks about larger cardinals are made; some questions of Gloede [9]are settled. Finally we argue that the evidence forV=Lis strong, and that CH is certainly true. MSC: 03E30, 03E55.

ISSN:0942-5616    

DOI:10.1002/malq.19930390111

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1993

数据来源: WILEY

摘要:

AbstractIn the present paper some tools are given to state the exact number of roots for some simple classes of exponential terms (with one variable). The result were obtained by generalizing Sturm's technique for real closed fields. Moreover for arbitrary non‐zero termst(x) certain estimations concerning the location of roots oft(x) are given. MSC: 03C65, 03C60, 12L1

ISSN:0942-5616    

DOI:10.1002/malq.19930390112

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1993

数据来源: WILEY