Club Guessing and the Universal Models
نویسنده
چکیده
We survey the use of club guessing and other pcf constructs in the context of showing that a given partially ordered class of objects does not have a largest, or a universal element. 1
منابع مشابه
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We examine the existence of universal elements in classes of infinite abelian groups. The main method is using group invariants which are defined relative to club guessing sequences. We prove, for example: Theorem: For n ≥ 2, there is a purely universal separable p-group in אn if, and only if, 20 ≤ אn. §0 Introduction In this paper “group” will always mean “infinite abelian group”, and “cardina...
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We examine the existence of universal elements in classes of innnite abelian groups. The method is deening some invariant of a group relative to a club guessing sequence, a combinatorial tool marketed here to algebraists. We prove, for example: Theorem: For n 2, there is a purely universal separable p-group in @ n if, and only if, 2 @ 0 @ n. + < < @ 0 , then there is no universal separable p-gr...
متن کامل1 4 A ug 2 00 6 Club guessing and the universal models Mirna Džamonja School of Mathematics University of East Anglia Norwich , NR 4 7 TJ , UK
We survey the use of club guessing and other pcf constructs in the context of showing that a given partially ordered class of objects does not have a largest, or a universal element. 1 0 Introduction A natural problem in mathematics is the following: given some partially ordered or a quasi-ordered set or a class, is there the largest element in it. An aspect of this question appears in the theo...
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In his book on Pmax [6], Woodin presents a collection of partial orders whose extensions satisfy strong club guessing principles on ω1. In this paper we employ one of the techniques from this book to produce Pmax variations which separate various club guessing principles. The principle (+) and its variants are weak guessing principles which were first considered by the second author [3] while s...
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We shall show that the consistency of CH+¬(+) and CH+(+)+there are no club guessing sequences on ω1. We shall also prove that ♢ does not imply the existence of a strong club guessing sequence on ω1. §0. Introduction. The principle (+) and its variations were first considered by the second author in [2]. They are very weak club guessing principles. The properties of the principles were largely u...
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ورودعنوان ژورنال:
- Notre Dame Journal of Formal Logic
دوره 46 شماره
صفحات -
تاریخ انتشار 2005