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

• Ano de defesa: 2022
• Autor(a) principal: Carvalho, Rodrigo Rey
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Covering properties; Elementary submodels; Espaços de funções; Forcing; Function spaces; Partição de espaços topológicos; Propriedades de cobertura; Ramsey theory; Submodelos elementares; Teoria de Ramsey; Topological space partitions
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/45/45131/tde-12102022-112918/

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.