Martínez Alonso, Juan CarlosSoukup, Lajos2023-02-242023-02-242022-09-200016-2736https://hdl.handle.net/2445/194104We construct locally Lindelöf scattered P-spaces (LLSP spaces, for short) with prescribed widths and heights under different set-theoretic assumptions. We prove that there is an LLSP space of width $\omega_1$ and height $\omega_2$ and that it is relatively consistent with ZFC that there is an LLSP space of width $\omega_1$ and height $\omega_3$. Also, we prove a stepping up theorem which, for every cardinal $\lambda \geq \omega_2$, permits us to construct from an LLSP space of width $\omega_1$ and height $\lambda$ satisfying certain additional properties an LLSP space of width $\omega_1$ and height $\alpha$ for every ordinal $\alpha<\lambda^{+}$. As consequences of the above results, we obtain the following theorems: (1) For every ordinal $\alpha<\omega_3$ there is an LLSP space of width $\omega_1$ and height $\alpha$. (2) It is relatively consistent with ZFC that there is an LLSP space of width $\omega_1$ and height $\alpha$ for every ordinal $\alpha<\omega_4$.16 p.application/pdfeng(c) Institute of Mathematics, Polish Academy of Sciences, 2022Nombres cardinalsTeoria de conjuntsTopologiaEspais topològicsCardinal numbersSet theoryTopologyTopological spacesinfo:eu-repo/semantics/article7261032023-02-24info:eu-repo/semantics/openAccess