Covering properties,reflections in elementary submodels and partitions on topological spaces

• Autor(a) principal: Carvalho, Rodrigo Rey
• Data de Publicação: 2022
• Tipo de documento: Tese
• Idioma: eng
• Título da fonte: Biblioteca Digital de Teses e Dissertações da USP
• Texto Completo: https://www.teses.usp.br/teses/disponiveis/45/45131/tde-12102022-112918/
• topic: Covering properties; Elementary submodels; Espaços de funções; Forcing; Forcing; Function spaces; Partição de espaços topológicos; Propriedades de cobertura; Ramsey theory; Submodelos elementares; Teoria de Ramsey; Topological space partitions

This work develops two distinct topics. We first work with partitions on topological spaces, developing some topics found on [27]. We fixed the proof of the first theorem from the previous paper. We also improved the consistency of a result obtained using by constructing an example consistent with ¬. In relation with the second topic we studied the spaces developed on [25]. For this we followed the line of work of the thesis [16]. We see that, for scattered spaces the properties Rothberger, Menger and indestructibly Lindelöf are preserved for elementary submodels. Furthermore we continue to investigate these preservations for more general spaces. Finally we worked with spaces and elementary submodels.