The Nonabsoluteness of Model Existence in Uncountable Cardinals for Lω1,ω

被引：2

作者：

Friedman, Sy-David ^{[1
]}

Hyttinen, Tapani ^{[2
]}

Koerwien, Martin ^{[1
]}

机构：

[1] Kurt Godel Res Ctr Math Log, A-1090 Vienna, Austria

[2] Univ Helsinki, Dept Math, FI-00014 Helsinki, Finland

来源：

NOTRE DAME JOURNAL OF FORMAL LOGIC | 2013年 / 54卷 / 02期

基金：

奥地利科学基金会; 芬兰科学院;

关键词：

infinitary logic; absoluteness; abstract elementary classes;

D O I：

10.1215/00294527-1960443

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For sentences phi of L-omega 1,L-omega we investigate the question of absoluteness of phi having models in uncountable cardinalities. We first observe that having a model in N-1 is an absolute property, but having a model in N-2 is not as it may depend on the validity of the continuum hypothesis. We then consider the generalized continuum hypothesis (GCH) context and provide sentences for any alpha is an element of omega(1) \ {0, 1, omega} for which the existence of a model in N-alpha is nonabsolute (relative to large cardinal hypotheses). Finally, we present a complete sentence for which model existence in N-3 is nonabsolute.

引用

页码：137 / 151

页数：15

共 8 条

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[5] Kurepa trees and spectra of Lω1,ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {L}}_{\omega _1,\omega }$$\end{document}-sentences
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[8] On Transferring Model Theoretic Theorems of L∞,ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{L}_{{\infty},\omega}}$$\end{document} in the Category of Sets to a Fixed Grothendieck Topos
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Logica Universalis, 2014, 8 (3-4) : 345 - 391

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