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SACCHARINITY WITH ccc
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AI
DOI：10.1017/jsl.2026.10215.png)
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Abstract
En 中文
Using creature technology, we construct families of Suslin ccc non-sweet forcing notions Q $\mathbb Q$ double struck upper Q such that Z F C $ZFC$ upper Z upper F upper C is equiconsistent with Z F + $ZF+$ upper Z upper F plus "Every set of reals equals a Borel set modulo the ( <= aleph 1 ) $(\leq \aleph _1)$ left parenthesis less than or equals normal first transfinite cardinal 1 right parenthesis -closure of the null ideal associated with Q $\mathbb Q$ double struck upper Q " + $+$ plus "There is an omega 1 $\omega _1$ omega 1 -sequence of distinct reals." This answers a question of the second author and Kellner. As an application of independent interest, we also show how our forcing adds a new Pi 2 1 $\Pi <^>1_2$ normal upper Pi 2 Superscript 1 singleton over L without relying on L-combinatorics.
Keywords:
Suslin forcing
creature forcing
non-wellfounded iterations
regularity properties
Journal
J
IF:
0.6
Papers:
69
Citations:
0
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