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- W2888788110 abstract "We show that if $M$ is a countable transitive model of ZF and if $a,b$ are reals not in $M$, then there is a $G$ generic over $M$ such that $b in L[a,G]$. We then present several applications such as the following: if $J$ is any countable transitive model of ZFC and $M notsubseteq J$ is another countable transitive model of ZFC of the same ordinal height $alpha$, then there is a forcing extension $N$ of $J$ such that $M cup N$ is not included in any transitive model of ZFC of height $alpha$. Also, assuming $0^#$ exists, letting $S$ be the set of reals generic over $L$, although $S$ is disjoint from the Turing cone above $0^#$, we have that for any non-constructible real $a$, ${ a oplus s : s in S }$ is cofinal in the Turing degrees." @default.
- W2888788110 created "2018-09-07" @default.
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- W2888788110 date "2018-08-30" @default.
- W2888788110 modified "2023-09-26" @default.
- W2888788110 title "Generic Coding with Help and Amalgamation Failure" @default.
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- W2888788110 doi "https://doi.org/10.48550/arxiv.1808.10304" @default.
- W2888788110 hasPublicationYear "2018" @default.
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