
arXiv: math/9509208
In this paper we prove Jensen's Coding Theorem, assuming ˜ 0#, via a proof that makes no use of the fine structure theory. We do need to quote Jensen's Covering Theorem, whose proof uses fine-structural ideas, but make no direct use of these ideas. The key to our proof is the use of “coding delays.”Coding Theorem (Jensen). Suppose 〈M,A〉 is a model of ZFC + O#does not exist. Then there is an 〈M, A〉-definable class forcing P such that if G ⊆ P is P-generic over 〈M, A〉:(a) 〈M[G],A,G〉 ⊨ NZFC.(b) M[G] ⊨ V = L[R], R ⊆ ωand 〈M[G], A, G〉 ⊨ A,G are definable from the parameter R.In the above statement when we say “〈M, A〉 ⊨ ZFC” we mean that M ⊨ ZFC and in addition M satisfies replacement for formulas that mention A as a predicate. And “P-generic over 〈M, A〉” means that all 〈M, A〉-definable dense classes are met.The consequence of ˜ O# that we need follows directly from the Covering Theorem.
Other aspects of forcing and Boolean-valued models, covering theorem, Inner models, including constructibility, ordinal definability, and core models, FOS: Mathematics, Mathematics - Logic, 0 sharp, coding theorem, Logic (math.LO), fine structure
Other aspects of forcing and Boolean-valued models, covering theorem, Inner models, including constructibility, ordinal definability, and core models, FOS: Mathematics, Mathematics - Logic, 0 sharp, coding theorem, Logic (math.LO), fine structure
| selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | 1 | |
| popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network. | Average | |
| influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Average | |
| impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Average |
