More on countably compact,locally countable spaces |
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Authors: | I. Juhász S. Shelah L. Soukup |
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Affiliation: | (1) Mathematical Institute Hungarian Academy of Sciences, Budapest, Hungary;(2) Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel |
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Abstract: | Following [5], aT 3 spaceX is called good (splendid) if it is countably compact, locally countable (andω-fair).G(κ) (resp.S(κ)) denotes the statement that a good (resp. splendid) spaceX with |X|=κ exists. We prove here that (i) Con(ZF)→Con(ZFC+MA+2 ω is big+S(κ) holds unlessω=cf(κ)<κ); (ii) a supercompact cardinal implies Con(ZFC+MA+2suω>ω+1+┐G(ωω+1); (iii) the “Chang conjecture” (ωω+1),→(ω 1,ω) implies ┐S(κ) for allκ≧k≧ωω; (iv) ifP addsω 1 dominating reals toV iteratively then, in , we haveG(λω) for allλ. Research supported by Hungarian National Foundation for Scientific Research grant no. 1805. |
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