Combining Philosophers

Ideas for H.Putnam/P.Oppenheim, Nicholas P. White and Wilfrid Hodges

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6 ideas

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

10473

Model theory studies formal or natural language-interpretation using set-theory [Hodges,W]

10475

A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W]

10481

Models in model theory are structures, not sets of descriptions [Hodges,W]

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

10288

Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model [Hodges,W]

17813

Löwenheim-Skolem says any theory with a true interpretation has a model in the natural numbers [White,NP]

10289

Up Löwenheim-Skolem: if infinite models, then arbitrarily large models [Hodges,W]