Ideas of Wilfrid Hodges, by Theme
[British, b.1941, Of Bedford College, then Queen Mary and Westfield, London.]
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2. Reason / D. Definition / 7. Contextual Definition
10476

The idea that groups of concepts could be 'implicitly defined' was abandoned

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)

5. Theory of Logic / A. Overview of Logic / 5. FirstOrder Logic
10478

Since firstorder languages are complete, = and  have the same meaning

5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence =
10477

= in modeltheory means 'logical consequence'  it holds in all models

5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
10285

I = φ means that the formula φ is true in the interpretation I

10283

A formula needs an 'interpretation' of its constants, and a 'valuation' of its variables

10284

There are three different standard presentations of semantics

5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
10474

= should be read as 'is a model for' or 'satisfies'

5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10473

Model theory studies formal or natural languageinterpretation using settheory

10475

A 'structure' is an interpretation specifying objects and classes of quantification

10481

Models in model theory are structures, not sets of descriptions

5. Theory of Logic / J. Model Theory in Logic / 3. LöwenheimSkolem Theorems
10289

Up LöwenheimSkolem: if infinite models, then arbitrarily large models

10288

Down LöwenheimSkolem: if a countable language has a consistent theory, that has a countable model

5. Theory of Logic / K. Features of Logics / 6. Compactness
10287

If a firstorder theory entails a sentence, there is a finite subset of the theory which entails it

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
10480

Firstorder logic can't discriminate between one infinite cardinal and another

6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10286

A 'set' is a mathematically wellbehaved class
