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Ideas of Marcus Rossberg, by Text

[German, fl. 2008, Professor at the University of Connecticut.]

2004 First-order Logic, 2nd-order, Completeness
1 p.303 Second-order logic needs the sets, and its consequence has epistemological problems
2 p.304 Γ|-S says S can be deduced from Γ; Γ|=S says a good model for Γ makes S true
2 p.305 Logical consequence is intuitively semantic, and captured by model theory
2 p.306 In proof-theory, logical form is shown by the logical constants
3 p.306 A model is a domain, and an interpretation assigning objects, predicates, relations etc.
3 p.306 A deductive system is only incomplete with respect to a formal semantics
3 p.307 Henkin semantics has a second domain of predicates and relations (in upper case)
3 p.307 If models of a mathematical theory are all isomorphic, it is 'categorical', with essentially one model
3 p.308 There are at least seven possible systems of semantics for second-order logic
4 p.315 With possible worlds, S4 and S5 are sound and complete, but S1-S3 are not even sound
5 p.317 Completeness can always be achieved by cunning model-design