摘要:

AbstractWe construct an r. e. degree a which possesses a greatest a‐minimal pair b0, b1, i.e., r. e. degrees b0and b1such that b0, b1

ISSN:0942-5616    

DOI:10.1002/malq.19940400302

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1994

数据来源: WILEY

摘要:

AbstractWe prove that every convexly ordered valuation ring has a unique completion as a uniform space, which furthermore is a convexly ordered valuation ring. In addition, we give a model theoretic characterisation of complete convexly ordered valuation rings, and give a necessary and sufficient condition for the completion of a convexly ordered valuation ring to be a real closed ring.Mathematics Subject Classification: 03C60, 13L05, 54E15.

ISSN:0942-5616    

DOI:10.1002/malq.19940400303

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1994

数据来源: WILEY

摘要:

AbstractIn this paper we show that the prime ideal space of an MV‐algebra is the disjoint union of prime ideal spaces of suitable local MV‐algebras. Some special classes of algebras are defined and their spaces are investigated. The space of minimal prime ideals is studied as well.Mathematics Subject Classification: 03B50, 06

ISSN:0942-5616    

DOI:10.1002/malq.19940400304

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1994

数据来源: WILEY

摘要:

AbstractWe prove a theorem about models with indiscernibles that are cofinal in a given linear order. We apply this theorem to obtain new independence results for Quine's set theory New Foundations, thus solving two open problems in this field.Mathematics Subject Classification: 03C55, 03B15, 03B60, 03E70.

ISSN:0942-5616    

DOI:10.1002/malq.19940400305

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1994

数据来源: WILEY

摘要:

AbstractLetSbe a set,P(S) the class of all subsets ofSandF(S) the class of all fuzzy subsets ofS.In this paper an “extension principle” for closure operators and, in particular, for deduction systems is proposed and examined. Namely we propose a way to extend any closure operator J defined inP(S) into a fuzzy closure operator J* defined inF(S). This enables us to give the notion of canonical extension of a deduction system and to give interesting examples of fuzzy logics. In particular, the canonical extension of the classical propositional calculus is defined and it is showed its connection with possibility and necessity measures. Also, the canonical extension of first order logic enables us to extend some basic notions of programming logic, namely to define the fuzzy Herbrand models of a fuzzy program. Finally, we show that the extension principle enables us to obtain fuzzy logics related to fuzzy subalgebra theory and graded consequence relation theory.Mathematics Subject Classification: 03

ISSN:0942-5616    

DOI:10.1002/malq.19940400306

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1994

数据来源: WILEY

摘要:

AbstractWe study game formulas the truth of which is determined by a semantical game of uncountable length. The main theme is the study of principles stating reflection of these formulas in various admissible sets. This investigation leads to two weak forms of strict‐II11reflection (or ∑1‐compactness). We show that admissible sets such asH(ω2) andLω2which fail to have strict‐II11reflection, may or may not, depending on set‐theoretic hypotheses satisfy one or both of these weaker forms.Mathematics Subject Classification: 0

ISSN:0942-5616    

DOI:10.1002/malq.19940400307

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1994

数据来源: WILEY

摘要:

AbstractWe give a plausible‐sounding conjecture involving the number ofn‐equivalence classes of structures of sizemwhich would imply that the complement of a spectrum is also a spectrum.Mathematics Subject Classification: 03B10, 03D15, 68

ISSN:0942-5616    

DOI:10.1002/malq.19940400308

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1994

数据来源: WILEY

摘要:

AbstractIn this paper we establish the (1, 2)‐ and (2, 1)‐transfer principles for finitely decidable locally finite varieties, where a class of structures is finitely decidable if the first order theory of its finite members is recursive. The transfer principles deal with the local structure of finite algebras and have strong global consequences.Mathematics Subject Classification: 08A05, 03C13, 08B05, 08

ISSN:0942-5616    

DOI:10.1002/malq.19940400309

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1994

数据来源: WILEY

摘要:

AbstractIt is easy to prove in ZF−(= Zermelo‐Fraenkel set theory without the axioms of choice and foundation) that a relationRsatisfies the maximal condition if and only if its transitive hullR* does; equivalently:Ris well‐founded if and only ifR* is. We will show in the following that, if the maximal condition is replaced by the (finite ascending) chain condition, as is often the case in Algebra, the resulting statement is not provable in ZF−anymore (if ZF−is consistent). More precisely, we will prove that this statement is equivalent in ZF−to the countable axiom of choice ACω. Moreover, applying this result we will prove that the axiom of dependent choices,restricted to partial ordersas used in Algebra, already implies the general form for arbitrary relations as formulated first by Teichmüller and, independently, some time later by Bernays and Tarski.Mathematics Subject Classification: 06B05, 08A65,

ISSN:0942-5616    

DOI:10.1002/malq.19940400310

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1994

数据来源: WILEY

摘要:

AbstractWe sketch proofs of the theorems of Church‐Turing and Trachtenbrot using a semi‐monomorphic axiomatization.Mathematics Subject Classification: 03B10, 03

ISSN:0942-5616    

DOI:10.1002/malq.19940400311

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1994

数据来源: WILEY