摘要:

AbstractIn this paper we characterize the MV‐algebras containing as subalgebras Post algebras of finitely many orders. For this we study cyclic elements in MV‐algebras which are the generators of the fundamental chain of the Post algebras.Mathematics Subject Classification:03G20, 03G25, 06D25, 06D30, 06F15, 06

ISSN:0942-5616    

DOI:10.1002/malq.19940400402

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1994

数据来源: WILEY

摘要:

AbstractWe recall the characterisation of positive definite polynomial functions over a real closed ring due to Dickmann, and give a new proof of this result, based upon ideas of Abraham Robinson. In addition we isolate the class of convexly ordered valuation rings for which this characterisation holds.Mathematics Subject Classification:03C60, 13L05, 12D15.

ISSN:0942-5616    

DOI:10.1002/malq.19940400403

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 of metric‐Euclidean and of rectangular planes (generalizations of Euclidean planes). The languages in which the axiom systems are expressed contain three individual constants and two ternary operations. We also provide an axiom system in algorithmic logic for finite Euclidean planes, and for several minimal metric‐Euclidean planes. The axiom systems proposed will be used in a sequel to this paper to provide ‘the simplest possible’ axiom systems for several fragments of plane Euclidean geometry.Mathematics Subject Classification:51M05, 51M

ISSN:0942-5616    

DOI:10.1002/malq.19940400404

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1994

数据来源: WILEY

摘要:

AbstractIn the present note we give a direct deduction of the Axiom of Choice from the Maximal Ideal Theorem for commutative rings with unit.Mathematics Subject Classification:03E25, 04A25, 13A15.

ISSN:0942-5616    

DOI:10.1002/malq.19940400405

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1994

数据来源: WILEY

摘要:

AbstractWe prove the cut‐elimination theorem, Gentzen's Hauptsatz, for the system for stratified comprehension, i. e. Quine's NF minus extensionality.Mathematics Subject Classification:03B15, 03F0

ISSN:0942-5616    

DOI:10.1002/malq.19940400406

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1994

数据来源: WILEY

摘要:

AbstractWe investigate the upper semilattice Eq* of recursively enumerable equivalence relations modulo finite differences. Several natural subclasses are shown to be first‐order definable in Eq*. Building on this we define a copy of the structure of recursively enumerable many‐one degrees in Eq*, thereby showing that Th(Eq*) has the same computational complexity as the true first‐order arithmetic.Mathematics Subject Classification:03D25, 03D15,

ISSN:0942-5616    

DOI:10.1002/malq.19940400407

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1994

数据来源: WILEY

摘要:

AbstractThe constructive functional calculus for a sequence of commuting selfadjoint operators on a separable Hilbert space is shown to be independent of the orthonormal basis used in its construction. The proof requires a constructive criterion for the absolute continuity of two positive measures in terms of test functions.Mathematics Subject Classification:03F60, 46S30, 47S30.

ISSN:0942-5616    

DOI:10.1002/malq.19940400408

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1994

数据来源: WILEY

摘要:

AbstractWe give a proof of Gödel's first incompleteness theorem based on Berry's paradox, and from it we also derive the second incompleteness theorem model‐theoretically.Mathematics Subject Classification:03F

ISSN:0942-5616    

DOI:10.1002/malq.19940400409

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1994

数据来源: WILEY

摘要:

AbstractThe present article deals with the power of the axiom of choice (AC) within the second‐order predicate logic. We investigate the relationship between several variants of AC and some other statements, known as equivalent to AC within the set theory of Zermelo and Fraenkel with atoms, in Henkin models of the one‐sorted second‐order predicate logic with identity without operation variables. The construction of models follows the ideas of Fraenkel and Mostowski. It is e. g. shown that the well‐ordering theorem for unary predicates is independent from AC for binary predicates and from the trichotomy law for unary predicates. Moreover, we show that the AC for binary predicates follows neither from the trichotomy law for unary predicates nor from Zorn's lemma for unary predicates nor from the formalization of the axiom of choice for disjoint families of sets for binary predicates, and that the trichotomy law for unary predicates does not follow from AC for binary predicates.Mathematics Subject Classification:03B15, 03E25

ISSN:0942-5616    

DOI:10.1002/malq.19940400410

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1994

数据来源: WILEY

摘要:

AbstractWe present the axioms of Alternative Set Theory (AST) in the language of second‐order arithmetic and study its ω‐ and β‐models. These are expansions of the form (M,M),M⊆P(M), of nonstandard modelsMof Peano arithmetic (PA) such that (M,M) ⊩ AST and ω ϵM. Our main results are: (1) A countableM⊩ PA is β‐expandable iff there is a regular well‐ordering forM.(2) Every countable β‐model can be elementarily extended to an ω‐model which is not a β‐model. (3) The Ω‐orderings of an ω‐model (M,M) are absolute well‐orderings iff the standard system SS(M) ofMis a β‐model of A−2.(4) There are ω‐expandable modelsMsuch that no ω‐expansion ofMcontains absolute Ω‐orderings. (5) There are s‐expandable models (i. e., their ω‐expansions contain only absolute Ω‐orderings) which are not β‐expandable. (6) For every countable β‐expansionMofM, there is a generic extensionM[G] which is also a β‐expansion ofM.(7) IfMis countable and β‐expandable, then there are regular orderings<1,<2such that neither<1belongs to the ramified analytical hierarchy of the structure (M,<2), nor<2to that of (M,<1). (8) The result (1) can be improved as follows: A counta

ISSN:0942-5616    

DOI:10.1002/malq.19940400411

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1994

数据来源: WILEY