文摘
Starting from infinitely many supercompact cardinals, we force a model of ZFC where class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S016800721630032X&_mathId=si1.gif&_user=111111111&_pii=S016800721630032X&_rdoc=1&_issn=01680072&md5=a737f9698a36da60d0b63b96833a4d92" title="Click to view the MathML source">ℵω2+1class="mathContainer hidden">class="mathCode"> satisfies simultaneously a strong principle of reflection, called Δ-reflection, and a version of the square principle, denoted class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S016800721630032X&_mathId=si10.gif&_user=111111111&_pii=S016800721630032X&_rdoc=1&_issn=01680072&md5=3778a603a690d180e010418fed78703d" title="Click to view the MathML source">□(ℵω2+1)class="mathContainer hidden">class="mathCode">. Thus we show that class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S016800721630032X&_mathId=si1.gif&_user=111111111&_pii=S016800721630032X&_rdoc=1&_issn=01680072&md5=a737f9698a36da60d0b63b96833a4d92" title="Click to view the MathML source">ℵω2+1class="mathContainer hidden">class="mathCode"> can satisfy simultaneously a strong reflection principle and an anti-reflection principle.