Permutation Models of Second Order
Christine Ga{\ss}ner
TL;DR
This paper explores second-order permutation models, extending the Fraenkel-Mostowski-Specker method to analyze the strength of second-order choice principles in predicate logic with Henkin semantics.
Contribution
It introduces an extension of the second-order permutation models and applies it to study the strength of second-order choice principles in HPL.
Findings
Extended the Fraenkel-Mostowski-Specker method for second-order models
Analyzed the strength of second-order choice principles in HPL
Discussed implications for models of ZFA and related logic systems
Abstract
G\"unter Asser (1981) introduced second-order permutation models. In this way, the Fraenkel-Mostowski-Specker method for defining models of ZFA was transferred to a new application area. To investigate the strength of second-order principles of choice in second-order predicate logic (PLII) with Henkin interpretation (HPL), we have extended the Fraenkel-Mostowski-Specker-Asser method. Here we discuss many details, including some useful references. Finally, we address a question raised by Stephen Mackereth.
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Taxonomy
Topicssemigroups and automata theory