Topološke lastnosti so logični principi v topoloških modelih : magistrsko delo

Strah, Luna (author), Bauer, Andrej (mentor)

Delo obravnava odvisnost med topološkimi lastnostmi danega prostora in logičnimi principi, ki veljajo v topološkem modelu nad prostorom. Najprej definiramo topološke modele in interpretacijo intuicionistične logike delnih elementov v takih modelih. Nato obravnavamo znane principe izbire in odločjivosti, ki v intuicionistični logiki niso dokazljivi. V osrednjem delu analiziramo, kakšen je odnos med topološkimi lastnostmi prostora in veljavnostjo principov v topološkem modelu nad prostorom.

• Language: Slovenian
• Keywords: topološki modeli, konstruktivna logika
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2025
• PID: 20.500.12556/RUL-173506
• UDC: 510.6
• COBISS.SI-ID: 249053187
• Publication date in RUL: 18.09.2025

Secondary language

• Language: English
• Title: Topological properties are logical principles in topological models

Abstract

In this thesis we study the relationship between the topological properties of a given space and logical principles that hold in the topological model over this space. First we define topological models and the interpretation of intuitionistic logic of partial elements in such models. Next we study known principles of choice and decision that are not provable in intuitionistic logic. In the central part we analyse how topological properties of a space are related to the validity of various principles in the topological model over this space.

• Keywords: topological models, constructive logic