共查询到20条相似文献,搜索用时 15 毫秒
1.
Jan von Plato 《Archive for Mathematical Logic》2001,40(7):541-567
The structure of derivations in natural deduction is analyzed through isomorphism with a suitable sequent calculus, with
twelve hidden convertibilities revealed in usual natural deduction. A general formulation of conjunction and implication elimination
rules is given, analogous to disjunction elimination. Normalization through permutative conversions now applies in all cases.
Derivations in normal form have all major premisses of elimination rules as assumptions. Conversion in any order terminates.
Through the condition that in a cut-free derivation of the sequent Γ⇒C, no inactive weakening or contraction formulas remain in Γ, a correspondence with the formal derivability relation of natural
deduction is obtained: All formulas of Γ become open assumptions in natural deduction, through an inductively defined translation.
Weakenings are interpreted as vacuous discharges, and contractions as multiple discharges. In the other direction, non-normal
derivations translate into derivations with cuts having the cut formula principal either in both premisses or in the right
premiss only.
Received: 1 December 1998 / Revised version: 30 June 2000 / Published online: 18 July 2001 相似文献
2.
Continuing [6], [8] and [16], we study the consequences of the weak Freese-Nation property of (?(ω),⊆). Under this assumption,
we prove that most of the known cardinal invariants including all of those appearing in Cichoń's diagram take the same value
as in the corresponding Cohen model. Using this principle we could also strengthen two results of W. Just about cardinal sequences
of superatomic Boolean algebras in a Cohen model. These results show that the weak Freese-Nation property of (?(ω),⊆) captures
many of the features of Cohen models and hence may be considered as a principle axiomatizing a good portion of the combinatorics
available in Cohen models.
Received: 7 June 1999 / Revised version: 17 October 1999 /?Published online: 15 June 2001 相似文献
3.
Todd Eisworth 《Archive for Mathematical Logic》2001,40(3):235-242
We investigate a two-player game involving pairs of filters on ω. Our results generalize a result of Shelah ([7] Chapter
VI) dealing with applications of game theory in the study of ultrafilters.
Received: 28 September 1998 / Published online: 25 January 2001 相似文献
4.
Heike Mildenberger 《Archive for Mathematical Logic》2001,40(2):93-112
We show that the Filter Dichotomy Principle implies that there are exactly four classes of ideals in the set of increasing
functions from the natural numbers. We thus answer two open questions on consequences of ? < ?. We show that ? < ? implies
that ? = ?, and that Filter Dichotomy together with ? < ? implies ? < ?. The technical means is the investigation of groupwise
dense sets, ideals, filters and ultrafilters. With related techniques we prove the new inequality ?≤ cf(?).
Received: 9 October 1998 / Revised version: 18 August 1999 / Published online: 21 December 2000 相似文献
5.
Thierry Coquand 《Archive for Mathematical Logic》1998,37(3):143-147
Semantical arguments, based on the completeness theorem for first-order logic, give elegant proofs of purely syntactical
results. For instance, for proving a conservativity theorem between two theories, one shows instead that any model of one
theory can be extended to a model of the other theory. This method of proof, because of its use of the completeness theorem,
is a priori not valid constructively. We show here how to give similar arguments, valid constructively, by using Boolean models.
These models are a slight variation of ordinary first-order models, where truth values are now regular ideals of a given Boolean
algebra. Two examples are presented: a simple conservativity result and Herbrand's theorem.
Received December 5, 1995 相似文献
6.
Vladimir Kanovei 《Archive for Mathematical Logic》2001,40(8):615-628
We generalize, on higher projective levels, a construction of “incompatible” generic Δ1
3 real singletons given by Jensen and Johnsbr?ten.
Received: 3 November 1998 / Revised version: 23 April 2000 / Published online: 3 October 2001 相似文献
7.
Wilfried Buchholz 《Archive for Mathematical Logic》2001,40(4):255-272
Using the concept of notations for infinitary derivations we give an explanation of Takeuti's reduction steps on finite derivations (used in his consistency proof for Π1
1-CA) in terms of the more perspicious infinitary approach from [BS88].
Received: 27 April 1999 / Published online: 21 March 2001 相似文献
8.
We investigate several versions of a cardinal characteristic defined by Frankiewicz. Vojtáš showed , and Blass showed . We show that all the versions coincide and that is greater than or equal to the splitting number. We prove the consistency of and of .
Received: 2 October 1996 / Revised version: 22 May 1997 相似文献
9.
A class K of structures is controlled if, for all cardinals λ, the relation of L
∞,λ-equivalence partitions K into a set of equivalence classes (as opposed to a proper class). We prove that the class of doubly transitive linear orders
is controlled, while any pseudo-elementary class with the ω-independence property is not controlled.
Received: 23 September 1998 / Revised version: 6 July 1999 / Published online: 21 December 2000 相似文献
10.
We show that some cardinal arithmetic configurations related to the negation of the Shelah Weak Hypothesis and natural from
the forcing point of view are impossible.
Received: 8 September 1999 / Published online: 3 October 2001 相似文献
11.
In this paper we define a new condition number ?(A) for the following problem: given a m by n matrix A, find x∈ℝ
n
, s.t. Ax<0. We characterize this condition number in terms of distance to ill-posedness and we compare it with existing condition
numbers for the same problem.
Received: November 5, 1999 / Accepted: November 2000?Published online September 17, 2001 相似文献
12.
Let A≡KΔ /I be a factor of a path algebra. We develop a strategy to compute dim H
1(A), the dimension of the first Hochschild cohomology group of A, using combinatorial data from (Δ,I). That allows us to connect dim H
1(A) with the rank and p-rank of the fundamental group π1(Δ,I) of (Δ,I). We get explicit formulae for dim H
1(A), when every path in Δ parallel to an arrow belongs to I or when I is homogeneous.
Received: 12 April 1999 / Revised version: 9 October 2000 相似文献
13.
Silvio Valentini 《Archive for Mathematical Logic》2001,40(7):475-488
We provide a new and elementary proof of strong normalization for the lambda calculus of intersection types. It uses no strong
method, like for instance Tait-Girard reducibility predicates, but just simple induction on type complexity and derivation length and thus it is obviously formalizable within first order
arithmetic. To obtain this result, we introduce a new system for intersection types whose rules are directly inspired by the
reduction relation. Finally, we show that not only the set of strongly normalizing terms of pure lambda calculus can be characterized
in this system, but also that a straightforward modification of its rules allows to characterize the set of weakly normalizing
terms.
Received: 15 June 1998 / Revised version: 15 November 1999 / Published online: 15 June 2001 相似文献
14.
Marat M. Arslanov Iskander Sh. Kalimullin Andrea Sorbi 《Archive for Mathematical Logic》2001,40(8):597-614
We show that the Δ0
2 enumeration degrees are dense. We also show that for every nonzero n-c. e. e-degree a, with n≥ 3, one can always find a nonzero 3-c. e. e-degree b such that b < a on the other hand there is a nonzero ωc. e. e-degree which bounds no nonzero n-c. e. e-degree.
Received: 13 June 2000 / Published online: 3 October 2001 相似文献
15.
Radha Kessar 《manuscripta mathematica》2001,104(2):145-162
T. Jost proved that Donovan's conjecture holds for the unipotent blocks of the finite general linear groups over a fixed
field. In this paper, we show that the Morita equivalences exhibited by Jost are in fact equivalences between the source algebras
of the corresponding blocks, and thus that Puig's conjecture holds for the unipotent blocks of finite general groups over
a fixed field.
Received: 3 October 2000 相似文献
16.
17.
Jörg Brendle 《Monatshefte für Mathematik》2007,152(3):207-215
We show that
is consistent, where
is the groupwise density number and
is the groupwise density number for ideals. This answers a question of Heike Mildenberger.
Partially supported by Grant-in-Aid for Scientific Research (C) 17540116, Japan Society for the Promotion of Science. 相似文献
18.
We study the filter ℒ*(A) of computably enumerable supersets (modulo finite sets) of an r-maximal set A and show that, for some such set A, the property of being cofinite in ℒ*(A) is still Σ0
3-complete. This implies that for this A, there is no uniformly computably enumerable “tower” of sets exhausting exactly the coinfinite sets in ℒ*(A).
Received: 6 November 1999 / Revised version: 10 March 2000 /?Published online: 18 May 2001 相似文献
19.
Arthur W. Apter 《Archive for Mathematical Logic》2000,39(3):209-211
We give a new proof using iterated Prikry forcing of Magidor's theorem that it is consistent to assume that the least strongly
compact cardinal is the least supercompact cardinal.
Received: 8 December 1997 / Revised version: 12 November 1998 相似文献
20.
Paul Corazza 《Archive for Mathematical Logic》2000,39(3):219-226
The Wholeness Axiom (WA) is an axiom schema that can be added to the axioms of ZFC in an extended language , and that asserts the existence of a nontrivial elementary embedding . The well-known inconsistency proofs are avoided by omitting from the schema all instances of Replacement for j-formulas. We show that the theory ZFC + V = HOD + WA is consistent relative to the existence of an embedding. This answers a question about the existence of Laver sequences for regular classes of set embeddings: Assuming there is an -embedding, there is a transitive model of ZFC +WA + “there is a regular class of embeddings that admits no Laver sequence.”
Received: 7 July 1998 / Revised version: 5 November 1998 相似文献