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Ideas of Marcus Rossberg, by Text
[German, fl. 2008, Professor at the University of Connecticut.]
2004

Firstorder Logic, 2ndorder, Completeness

§1

p.303

10751

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

§2

p.304

10752

Γ  S says S can be deduced from Γ; Γ = S says a good model for Γ makes S true

§2

p.305

10753

Logical consequence is intuitively semantic, and captured by model theory

§2

p.306

10754

In prooftheory, logical form is shown by the logical constants

§3

p.306

10756

A model is a domain, and an interpretation assigning objects, predicates, relations etc.

§3

p.306

10755

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

§3

p.307

10758

If models of a mathematical theory are all isomorphic, it is 'categorical', with essentially one model

§3

p.307

10757

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

§3

p.308

10759

There are at least seven possible systems of semantics for secondorder logic

§5

p.317

10761

Completeness can always be achieved by cunning modeldesign
