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
10283

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

10284

There are three different standard presentations of semantics

10285

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

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
10475

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

10473

Model theory studies formal or natural languageinterpretation using settheory

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
