منابع مشابه
Thorn-forking as Local Forking
We introduce the notion of a preindependence relation between subsets of the big model of a complete first-order theory, an abstraction of the properties which numerous concrete notions such as forking, dividing, thorn-forking, thorn-dividing, splitting or finite satisfiability share in all complete theories. We examine the relation between four additional axioms (extension, local character, fu...
متن کاملA Geometric Introduction to Forking and Thorn-forking
A ternary relation |̂ between subsets of the big model of a complete first-order theory T is called an independence relation if it satisfies a certain set of axioms. The primary example is forking in a simple theory, but o-minimal theories are also known to have an interesting independence relation. Our approach in this paper is to treat independence relations as mathematical objects worth study...
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Spikes form an interesting class of 3-connected matroids of branch-width 3. We show that some computational problems are hard on spikes with given matrix representations over infinite fields. Namely, the question whether a given spike is the free spike is co-NP -hard (though the property itself is definable in monadic second-order logic); and the task to compute the Tutte polynomial of a spike ...
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Editor's Note: These short, critical reviews of recent papers in the Journal, written exclusively by graduate students or postdoctoral fellows, are intended to summarize the important findings of the paper and provide additional insight and commentary. For more information on the format and purpose of the Journal Club, please see What is the language of the brain when it links perception and be...
متن کاملLecture Notes on Forking
1.1. Types. Most of the time we fix a complete countable first-order theory T in a language L, and we let M be a very saturated model of it, a “monster” model. All our sets and models are subsets and elementary submodels of M. A set is called small if it is cardinality is smaller than the saturation of M. For a set A, we let Def (A) be the boolean algebra of A-definable subsets of M, i.e. sets ...
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ژورنال
عنوان ژورنال: Botanical Gazette
سال: 1876
ISSN: 0006-8071
DOI: 10.1086/325005