Souslin forcing

Journal of Symbolic Logic 53 (4):1188-1207 (1988)
We define the notion of Souslin forcing, and we prove that some properties are preserved under iteration. We define a weaker form of Martin's axiom, namely MA(Γ + ℵ 0 ), and using the results on Souslin forcing we show that MA(Γ + ℵ 0 ) is consistent with the existence of a Souslin tree and with the splitting number s = ℵ 1 . We prove that MA(Γ + ℵ 0 ) proves the additivity of measure. Also we introduce the notion of proper Souslin forcing, and we prove that this property is preserved under countable support iterated forcing. We use these results to show that ZFC + there is an inaccessible cardinal is equiconsistent with ZFC + the Borel conjecture + Σ 1 2 -measurability
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DOI 10.2307/2274613
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References found in this work BETA
D. A. Martin & R. M. Solovay (1970). Internal Cohen Extensions. Annals of Mathematical Logic 2 (2):143-178.

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Citations of this work BETA
Haim Judah, Saharon Shelah & W. H. Woodin (1990). The Borel Conjecture. Annals of Pure and Applied Logic 50 (3):255-269.
Boban Veličković (2009). Maharam algebras. Annals of Pure and Applied Logic 158 (3):190-202.
James Hirschorn (2009). A Strong Antidiamond Principle Compatible With. Annals of Pure and Applied Logic 157 (2):161-193.

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