SQUARE WITH BUILT-IN DIAMOND-PLUS. (8th September 2017)

• Record Type: Journal Article
• Authors: RINOT, ASSAF; SCHINDLER, RALF
• Is Part Of: Journal of symbolic logic. Volume 82:Number 3(2017)
• Page Start: 809
• Page End: 833
• Publication Date: 2017-09-08
• Subjects: Primary 03E45, -- Secondary 03E05; diamond principle, -- square principle, -- constructibility, -- walks on ordinals, -- Kurepa tree, -- almost Souslin tree, -- parameterized proxy principle; Logic, Symbolic and mathematical -- Periodicals; 511.3
• DOI: 10.1017/jsl.2016.69
• Languages: English
• ISSNs: 0022-4812

Abstract

Abstract: We formulate combinatorial principles that combine the square principle with various strong forms of the diamond principle, and prove that the strongest amongst them holds in L for every infinite cardinal. As an application, we prove that the following two hold in L : 1. For every infinite regular cardinal λ, there exists a special λ + -Aronszajn tree whose projection is almost Souslin; 2. For every infinite cardinal λ, there exists a respecting λ + -Kurepa tree; Roughly speaking, this means that this λ + -Kurepa tree looks very much like the λ + -Souslin trees that Jensen constructed in L .