Combining Texts

Ideas for 'Universal Prescriptivism', 'First-Order Logic' and 'Realistic Rationalism'

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7 ideas

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic

10282

Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former) [Hodges,W]

5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic

10283

A formula needs an 'interpretation' of its constants, and a 'valuation' of its variables [Hodges,W]

10284

There are three different standard presentations of semantics [Hodges,W]

10285

I |= φ means that the formula φ is true in the interpretation I [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]

10289

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

5. Theory of Logic / K. Features of Logics / 6. Compactness

10287

If a first-order theory entails a sentence, there is a finite subset of the theory which entails it [Hodges,W]