Ideas of Marcus Rossberg, by Theme

[German, fl. 2008, Professor at the University of Connecticut.]

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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