Ideas from 'Firstorder Logic, 2ndorder, Completeness' by Marcus Rossberg [2004], by Theme Structure
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5. Theory of Logic / A. Overview of Logic / 7. SecondOrder Logic
10751

Secondorder logic needs the sets, and its consequence has epistemological problems

10757

Henkin semantics has a second domain of predicates and relations (in upper case)

10759

There are at least seven possible systems of semantics for secondorder 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
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In prooftheory, logical form is shown by the logical constants

5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
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A model is a domain, and an interpretation assigning objects, predicates, relations etc.

5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
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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
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Completeness can always be achieved by cunning modeldesign

5. Theory of Logic / K. Features of Logics / 5. Incompleteness
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A deductive system is only incomplete with respect to a formal semantics
