Ideas from 'Firstorder Logic, 2ndorder, 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 S1S3 are not even sound

5. Theory of Logic / A. Overview of Logic / 7. SecondOrder Logic
10757

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

10751

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

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

ΓS 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 prooftheory, 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 modeldesign

5. Theory of Logic / K. Features of Logics / 5. Incompleteness
10755

A deductive system is only incomplete with respect to a formal semantics
