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Ideas of Marcus Rossberg, by Text
[German, fl. 2008, Professor at the University of Connecticut.]
2004
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First-order Logic, 2nd-order, Completeness
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§1
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p.303
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10751
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Second-order logic needs the sets, and its consequence has epistemological problems
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§2
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p.304
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10752
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Γ |- S says S can be deduced from Γ; Γ |= S says a good model for Γ makes S true
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§2
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p.305
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10753
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Logical consequence is intuitively semantic, and captured by model theory
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§2
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p.306
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10754
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In proof-theory, logical form is shown by the logical constants
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§3
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p.306
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10756
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A model is a domain, and an interpretation assigning objects, predicates, relations etc.
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§3
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p.306
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10755
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A deductive system is only incomplete with respect to a formal semantics
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§3
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p.307
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10758
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If models of a mathematical theory are all isomorphic, it is 'categorical', with essentially one model
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§3
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p.307
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10757
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Henkin semantics has a second domain of predicates and relations (in upper case)
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§3
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p.308
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10759
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There are at least seven possible systems of semantics for second-order logic
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§5
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p.317
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10761
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Completeness can always be achieved by cunning model-design
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