15,630 research outputs found
On Rules and Parameter Free Systems in Bounded Arithmetic
We present model–theoretic techniques to obtain conservation
results for first order bounded arithmetic theories, based on a hierarchical
version of the well known notion of an existentially closed model.Ministerio de Educación y Ciencia MTM2005-0865
Characterizations of pretameness and the Ord-cc
It is well known that pretameness implies the forcing theorem, and that
pretameness is characterized by the preservation of the axioms of
, that is without the power set axiom, or
equivalently, by the preservation of the axiom scheme of replacement, for class
forcing over models of . We show that pretameness in fact has
various other characterizations, for instance in terms of the forcing theorem,
the preservation of the axiom scheme of separation, the forcing equivalence of
partial orders and their dense suborders, and the existence of nice names for
sets of ordinals. These results show that pretameness is a strong dividing line
between well and badly behaved notions of class forcing, and that it is exactly
the right notion to consider in applications of class forcing. Furthermore, for
most properties under consideration, we also present a corresponding
characterization of the -chain condition
Class forcing, the forcing theorem and Boolean completions
The forcing theorem is the most fundamental result about set forcing, stating
that the forcing relation for any set forcing is definable and that the truth
lemma holds, that is everything that holds in a generic extension is forced by
a condition in the relevant generic filter. We show that both the definability
(and, in fact, even the amenability) of the forcing relation and the truth
lemma can fail for class forcing. In addition to these negative results, we
show that the forcing theorem is equivalent to the existence of a (certain kind
of) Boolean completion, and we introduce a weak combinatorial property
(approachability by projections) that implies the forcing theorem to hold.
Finally, we show that unlike for set forcing, Boolean completions need not be
unique for class forcing
A Combination Framework for Complexity
In this paper we present a combination framework for polynomial complexity
analysis of term rewrite systems. The framework covers both derivational and
runtime complexity analysis. We present generalisations of powerful complexity
techniques, notably a generalisation of complexity pairs and (weak) dependency
pairs. Finally, we also present a novel technique, called dependency graph
decomposition, that in the dependency pair setting greatly increases
modularity. We employ the framework in the automated complexity tool TCT. TCT
implements a majority of the techniques found in the literature, witnessing
that our framework is general enough to capture a very brought setting
Notions of denseness
The notion of a completely saturated packing [Fejes Toth, Kuperberg and
Kuperberg, Highly saturated packings and reduced coverings, Monats. Math. 125
(1998) 127-145] is a sharper version of maximum density, and the analogous
notion of a completely reduced covering is a sharper version of minimum
density. We define two related notions: uniformly recurrent and weakly
recurrent dense packings, and diffusively dominant packings. Every compact
domain in Euclidean space has a uniformly recurrent dense packing. If the
domain self-nests, such a packing is limit-equivalent to a completely saturated
one. Diffusive dominance is yet sharper than complete saturation and leads to a
better understanding of n-saturation.Comment: Published in Geometry and Topology at
http://www.maths.warwick.ac.uk/gt/GTVol4/paper9.abs.htm
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