In V [G], every set x ⊆ [ω]ω that belongs to L(R) is H-Ramsey for every happy family H ∈ V [G]. Consequently, there are no infinite mad families in L(R)V [G].
happy and mad families in l(r) - Cambridge University Press
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Abstract. We prove that, in the choiceless Solovay model, every set of reals is H-Ramsey for every happy family H that also belongs to the Solovay model.
HAPPY AND MAD FAMILIES IN L(ℝ) | The Journal of Symbolic Logic
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Aug 1, 2018 · This gives a new proof of Törnquist's recent theorem that there are no infinite mad families in the Solovay model. We also investigate happy ...
We prove that, in the choiceless Solovay model, every set of reals is H -Ramsey for every happy family H that also belongs to the Solovay model.
Certain infinite combinatorial structures in modern mathematics, called mad families, are known to exist only due to indirect, nonconstructive methods ...
CO-ANALYTIC MAD FAMILIES AND DEFINABLE WELLORDERS. 3. The method of [BK12] involved the construction of an ℵ1-perfect mad family in L, which had a. Σ1. 2 ...
Certain infinite combinatorial structures in modern mathematics, called mad families, are known to exist only due to indirect, nonconstructive methods ...
If s is a MAD family such that Id [ PI = c for every non-trivial partitioner P then there is a connected MAD family 66 such that J(s) = J(r). In fact, there ...
Jun 28, 2024 · [NN18] Itay Neeman and Zach Norwood, Happy and mad families in l(R), The. Journal of Symbolic Logic 83 (2018), no. 2, 572–597. [ST19] David ...
Dec 30, 2019 · ... MAD family can be an element of L(R); and under the Axiom of ... [6] Itay Neeman and Zach Norwood, Happy and mad families in L(R), J.