Square and Delta reflection

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• 作者：Laura Fontanella ; ^{laura.fontanella@mail.huji.ac.il" class="auth_mail" title="E-mail the corresponding author} ; Yair Hayut ; ^{yair.hayut@mail.huji.ac.il" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 03E55 ; 03E05 ; secondary ; 03E35 ; 03E65
• 刊名：Annals of Pure and Applied Logic
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：167
• 期：8
• 页码：663-683
• 全文大小：525 K

文摘

Starting from infinitely many supercompact cardinals, we force a model of ZFC where 032X&_mathId=si1.gif&_user=111111111&_pii=S016800721630032X&_rdoc=1&_issn=01680072&md5=a737f9698a36da60d0b63b96833a4d92" title="Click to view the MathML source">ℵ_ω²+1${\mathrm{\aleph }}_{{\omega }^2+1}$ satisfies simultaneously a strong principle of reflection, called Δ-reflection, and a version of the square principle, denoted 032X&_mathId=si10.gif&_user=111111111&_pii=S016800721630032X&_rdoc=1&_issn=01680072&md5=3778a603a690d180e010418fed78703d" title="Click to view the MathML source">□(ℵ_ω²+1)$\square ({\mathrm{\aleph }}_{{\omega }^2+1})$. Thus we show that 032X&_mathId=si1.gif&_user=111111111&_pii=S016800721630032X&_rdoc=1&_issn=01680072&md5=a737f9698a36da60d0b63b96833a4d92" title="Click to view the MathML source">ℵ_ω²+1${\mathrm{\aleph }}_{{\omega }^2+1}$ can satisfy simultaneously a strong reflection principle and an anti-reflection principle.