Fresh function spectra

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2023-10-01 DOI:10.1016/j.apal.2023.103300

Vera Fischer, Marlene Koelbing, Wolfgang Wohofsky

引用次数: 0

Abstract

In this paper, we investigate the fresh function spectrum of forcing notions, where a new function on an ordinal is called fresh if all its initial segments are in the ground model. We determine the fresh function spectrum of several forcing notions and discuss the difference between fresh functions and fresh subsets. Furthermore, we consider the question which sets are realizable as the fresh function spectrum of a homogeneous forcing. We show that under GCH all sets with a certain closure property are realizable, while consistently there are sets which are not realizable.

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新函数谱

在本文中，我们研究了强迫概念的新函数谱，其中如果序数上的新函数的所有初始段都在地面模型中，则称其为新函数。我们确定了几个强迫概念的新函数谱，并讨论了新函数和新子集之间的区别。此外，我们还考虑了哪些集合可以实现为齐次强迫的新函数谱的问题。我们证明了在GCH下，所有具有一定闭包性质的集合都是可实现的，而一致存在不可实现的集合。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of Pure and Applied Logic 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

200 days

期刊介绍： The journal Annals of Pure and Applied Logic publishes high quality papers in all areas of mathematical logic as well as applications of logic in mathematics, in theoretical computer science and in other related disciplines. All submissions to the journal should be mathematically correct, well written (preferably in English)and contain relevant new results that are of significant interest to a substantial number of logicians. The journal also considers submissions that are somewhat too long to be published by other journals while being too short to form a separate memoir provided that they are of particular outstanding quality and broad interest. In addition, Annals of Pure and Applied Logic occasionally publishes special issues of selected papers from well-chosen conferences in pure and applied logic.