摘要:

AbstractWe consider the problem of finding, in the ambit of modal logic, a minimal characterization for finite Kripke frames, i.e., a formula which, given a frame, axiomatizes its theory employing the lowest possible number of variables and implies the other axiomatizations. We show that every finite transitive frame admits a minimal characterization over K4, and that this result can not be extended to K.

ISSN:0942-5616    

DOI:10.1002/malq.19970430112

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1997

数据来源: WILEY

摘要:

AbstractWe first note that Gentzen's proof‐reduction for his consistency proof of PA can be directly interpreted as moves of Kirby‐Paris' Hydra Game, which implies a direct independence proof of the game (Section 1 and Appendix). Buchholz's Hydra Game for labeled hydras is known to be much stronger than PA. However, we show that the one‐dimensional version of Buchholz's Game can be exactly identified to Kirby‐Paris' Game (which is two‐dimensional but without labels), by a simple and natural interpretation (Section 2). Jervell proposed another type of a combinatorial game, by abstracting Gentzen's proof‐reductions and showed that his game is independent of PA. We show (Section 3) that this Jervell's game is actually much stronger than PA, by showing that the critical ordinal of Jervell's game is φω(0) (while that of PA or of Kirby‐Paris' Game is φ1(0) = ϵ0) in the Veblen hier

ISSN:0942-5616    

DOI:10.1002/malq.19970430113

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1997

数据来源: WILEY

摘要:

AbstractThis paper deals mainly with generalizations of results in finitary combinatorics to infinite ordinals. It is well‐known that for finite ordinals ∑bT<αβis the number of 2‐element subsets of an α‐element set. It is shown here that for any well‐ordered set of arbitrary infinite order type α, ∑bT<αβis the ordinal of the setMof 2‐element subsets, whereMis ordered in some natural way. The result is then extended to evaluating the ordinal of the set of alln‐element subsets for each natural numbern≥ 2. Moreover, series ∑β<αf(β) are investigated and evaluated, where α is a limit ordinal and the functionfbelongs to a certain class of functions containing polynomials with natural number coefficients. The tools developed for this result can be extended to cover all infinite α, but the case of finite α

ISSN:0942-5616    

DOI:10.1002/malq.19970430114

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1997

数据来源: WILEY

摘要:

AbstractIn the first part of this paper we letMbe a stable homogeneous model and we prove a nonstructure theorem for the class of all elementary submodels ofM, assuming thatMis ‘unsuperstable’ and has Skolem functions. In the second part we assume thatMis an unstable homogeneous model of large cardinality and we prove a nonstructure theorem for the class of all elementary submodels

ISSN:0942-5616    

DOI:10.1002/malq.19970430115

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1997

数据来源: WILEY

ISSN:0942-5616    

DOI:10.1002/malq.19970430101

出版商:WILEY‐VCH Verlag Berlin GmbH    

年代:1997

数据来源: WILEY