MoL-2011-14: Degrees of Non-Determinacy and Game Logics on Cardinals under the Axiom of Determinacy

MoL-2011-14: Li, Zhenhao (2011) Degrees of Non-Determinacy and Game Logics on Cardinals under the Axiom of Determinacy. [Report]

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Abstract

Degrees of Non-Determinacy and Game Logics on Cardinals under the Axiom of Determinacy Zhenhao Li Abstract: Blass showed that on each infinite cardinal, there is an algebra structure of games on it. Blass defined a reducibility relation on games via which he classified games into degrees of non-determinacy and proved nice properties of the degree structures on certain cardinals using the axiom of choice. Later Blass gave a game semantics to affine logic, an extension of linear logic, using his game algebra. He proved this game semantics is consistent (sound) but not complete. But he proved two nice completeness theorem for fragments of affine logic using the axiom of choice. This thesis gives a detailed exposition of Blass’s work on degree of non-determinacy and game semantics of linear logic, with an emphasis on the roles of cardinals and the usage of the axiom of choice, and contains our studies of degrees of non-determinacy and game logics on infinite cardinals in a set theory system without using the axiom of choice, namely in ZF with the axiom of determinacy.

Item Type: Report
Report Nr: MoL-2011-14
Series Name: Master of Logic Thesis (MoL) Series
Year: 2011
Date Deposited: 12 Oct 2016 14:38
Last Modified: 12 Oct 2016 14:38
URI: https://eprints.illc.uva.nl/id/eprint/859

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