### Ideas from 'First-order Logic, 2nd-order, Completeness' by Marcus Rossberg [2004], by Theme Structure

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###### 4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / a. Systems of modal logic
 10760 With possible worlds, S4 and S5 are sound and complete, but S1-S3 are not even sound
###### 5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
 10757 Henkin semantics has a second domain of predicates and relations (in upper case)
 10751 Second-order logic needs the sets, and its consequence has epistemological problems
 10759 There are at least seven possible systems of semantics for second-order logic
###### 5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
 10753 Logical consequence is intuitively semantic, and captured by model theory
###### 5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
 10752 Γ|-S says S can be deduced from Γ; Γ|=S says a good model for Γ makes S true
###### 5. Theory of Logic / E. Structures of Logic / 1. Logical Form
 10754 In proof-theory, logical form is shown by the logical constants
###### 5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
 10756 A model is a domain, and an interpretation assigning objects, predicates, relations etc.
###### 5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
 10758 If models of a mathematical theory are all isomorphic, it is 'categorical', with essentially one model
###### 5. Theory of Logic / K. Features of Logics / 4. Completeness
 10761 Completeness can always be achieved by cunning model-design
###### 5. Theory of Logic / K. Features of Logics / 5. Incompleteness
 10755 A deductive system is only incomplete with respect to a formal semantics