MoL-2016-23: Possibility Spaces, Q-Completions and Rasiowa-Sikorski Lemmas for Non-Classical Logics

MoL-2016-23: Massas, Guillaume (2016) Possibility Spaces, Q-Completions and Rasiowa-Sikorski Lemmas for Non-Classical Logics. [Report]

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Abstract

In this thesis, we study various generalizations and weakenings of the Rasiowa-Sikorski Lemma (Rasiowa-Sikorski) for Boolean algebras. Building on previous work from Goldblatt, we extend the Rasiowa-Sikorski Lemma to co-Heyting algebras and modal algebras, and show how this yields completeness results for the corresponding non-classical first-order logics. Moreover, working without the full power of the Axiom of Choice, we generalize the framework of possibility semantics from Humberstone, and more recently Holliday, in order to provide choice-free representation theorems for distributive lattice, Heyting algebras and co-Heyting algebras. We also generalize a weaker version of the Rasiowa-Sikorski Lemma for Boolean algebras, known as Tarski’s Lemma, to distributive lattices, HA’s and co-HA’s, and use these results to define a new semantics for first-order intuitionisitic logic.

Item Type: Report
Report Nr: MoL-2016-23
Series Name: Master of Logic Thesis (MoL) Series
Year: 2016
Subjects: Logic
Mathematics
Depositing User: Dr Marco Vervoort
Date Deposited: 02 Feb 2017 16:20
Last Modified: 02 Feb 2017 16:20
URI: https://eprints.illc.uva.nl/id/eprint/1522

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