Combining Texts

Ideas for 'Philosophy of Mathematics', 'On Metaphysics (frags)' and 'Introduction to Mathematical Logic'

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7 ideas

5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models

17747

A 'model' of a theory specifies interpreting a language in a domain to make all theorems true [Walicki]

10239

The central notion of model theory is the relation of 'satisfaction' [Shapiro]

10240

Model theory deals with relations, reference and extensions [Shapiro]

5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms

10214

Theory ontology is never complete, but is only determined 'up to isomorphism' [Shapiro]

10238

The set-theoretical hierarchy contains as many isomorphism types as possible [Shapiro]

5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems

17748

The L-S Theorem says no theory (even of reals) says more than a natural number theory [Walicki]

10234

Any theory with an infinite model has a model of every infinite cardinality [Shapiro]