摘要:

AbstractEvery model of IΔ0is the tally part of a model of the stringlanguage theory Th‐FO (a main feature of which consists in having induction on notation restricted to certainAC0. sets). We show how to “smoothly” introduce in Th‐FO the binary length function, whereby it is possible to make exponential assumptions in models of Th‐FO. These considerations entail that every model of IΔ0+ ¬exp is a proper initial segment of a model of Th‐FO and that amodicumof bounded collection is true in these models.Mathematics Subject Classification: 03F30

ISSN:0942-5616    

DOI:10.1002/malq.19960420102

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1996

数据来源: WILEY

摘要:

AbstractA hyperfinitely long coin flipping game between the Gambler and the Casino, associated with a given setA, is considered. It turns out that the Gambler has a winning strategy if and only ifAhas Loeb measure 0. The Casino has a winning strategy if and only ifAcontains an internal subset of positive Loeb measure.Mathematics Subject Classification:03H05, 03E15.

ISSN:0942-5616    

DOI:10.1002/malq.19960420103

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1996

数据来源: WILEY

摘要:

AbstractVector logic is a mathematical model of the propositional calculus in which the logical variables are represented by vectors and the logical operations by matrices. In this framework, many tautologies of classical logic are intrinsic identities between operators and, consequently, they are valid beyond the bivalued domain. The operators can be expressed as Kronecker polynomials. These polynomials allow us to show that many important tautologies of classical logic are generated from basic operators via the operations called Type I and Type II products. Finally, it is described a matrix version of the Fredkin gate that extends its properties to the many‐valued domain, and it is proved that the filtered Fredkin operators are second degree Kronecker polynomials that cannot be generated by Type I or Type II products.Mathematics Subject Classification:03B05, 03B5

ISSN:0942-5616    

DOI:10.1002/malq.19960420104

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1996

数据来源: WILEY

摘要:

AbstractThe problem is addressed of establishing the satisfiability of prenex formulas involving a single universal quantifier, in diversified axiomatic set theories. A rather general decision method for solving this problem is illustrated through the treatment of membership theories of increasing strength, ending with a subtheory of Zermelo‐Fraenkel which is already complete with respect to the ∀*∀ class of sentences. NP‐hardness and NP‐completeness results concerning the problems under study are achieved and a technique for restricting the universal quantifier is presented.Mathematics Subject Classification:03B

ISSN:0942-5616    

DOI:10.1002/malq.19960420105

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1996

数据来源: WILEY

摘要:

AbstractThe paper characterizes the second order arithmetic theorems of a set theory that features a recursively Mahlo universe; thereby complementing prior proof‐theoretic investigations on this notion. It is shown that the property of being recursively Mahlo corresponds to a certain kind of β‐model reflection in second order arithmetic. Further, this leads to a characterization of the reals recursively computable in the superjump functional.Mathematics Subject Classification:03F35, 03F15, 0

ISSN:0942-5616    

DOI:10.1002/malq.19960420106

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1996

数据来源: WILEY

摘要:

AbstractThe paper contains some observations on e‐complete, precomplete, and uniformly finitely precomplete r. e. equivalence relations. Among these are a construction of a uniformly finitely precomplete r. e. equivalence which is neither e‐ nor precomplete, an extension of Lachlan's theorem that all precomplete r. e. equivalences are isomorphic, and a characterization of sets of fixed points of endomorphisms of uniformly finitely precomplete r. e. equivalences.Mathematics Subject Classification:03

ISSN:0942-5616    

DOI:10.1002/malq.19960420107

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1996

数据来源: WILEY

摘要:

AbstractIn the present paper we prove that the isolated differences of r. e. degrees are dense in the r. e. degrees.Mathematics Subject Classification:03D25.

ISSN:0942-5616    

DOI:10.1002/malq.19960420108

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1996

数据来源: WILEY

摘要:

AbstractM. Forti and F. Honsell showed in [4] that the hyperuniverses defined in [2]satisfy the anti‐foundation axiomX1introduced in [3]. So it is interesting to study the axiomAFA, which is equivalent toX1in ZF, introduced by P. Aczel in [1]. We show in this paper thatAFAis inconsistent with the theory GPK. This theory, which is first order, is defined by E. Weydert in [6] and later by M. Forti and R. Hinnion in [2]. It includes all general hyperuniverses as defined in [5]. In order to achieve our aim, we need to define ordinals in GPK and to study some of their properties.Mathematics Subject Classification:03E70, 03E1

ISSN:0942-5616    

DOI:10.1002/malq.19960420109

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1996

数据来源: WILEY

摘要:

AbstractAn external characterization of the inductive sets on countable abstract structures is presented. The main result is an abstract version of the classical Suslin‐Kleene characterization of the hyperarithmetical sets.Mathematics Subject Classification:03D70, 03D7

ISSN:0942-5616    

DOI:10.1002/malq.19960420110

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1996

数据来源: WILEY

摘要:

AbstractWe consider some nonprincipal filters of the Medvedev lattice. We prove that the filter generated by the nonzero closed degrees of difficulty is not principal and we compare this filter, with respect to inclusion, with some other filters of the lattice. All the filters considered in this paper are disjoint from the prime ideal generated by the dense degrees of difficulty.Mathematics Subject Classification:03D30.

ISSN:0942-5616    

DOI:10.1002/malq.19960420111

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1996

数据来源: WILEY