2018/10/25 by Juan Carlos Martínez, Martínez, Juan Carlos, Lajos Soukup +1
Mathematics · #FOS: Mathematics #Logic (math.LO) #math.LO
paper · pdf · doi:10.48550/arxiv.1810.11052
arxiv created 2018/10/25 · arxiv updated 2018/10/29
We prove the following consistency result for cardinal sequences of length < \om3: if GCH holds and \la ≥ \om2 is a regular cardinal, then in some cardinal-preserving generic extension 2\om = \la and for every ordinal η< \om3 and every sequence f = ⟨ \ka\al : \al < η⟩ of infinite cardinals with \ka\al≤ \la for \al < η and \ka\al = \om if cf(\al) = \om2, we have that f is the cardinal sequence of some LCS space. Also, we prove that for every specific uncountable cardinal λ it is relatively consistent with ZFC that for every \al,\be < \om3 with cf(\al) < \om2 there is an LCS space Z such that CS(Z) = ⟨ ω⟩α\concat ⟨ λ⟩β.