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Single Idea 10286

[filed under theme 6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory ]

Full Idea

A 'set' is a mathematically well-behaved class.

Gist of Idea

A 'set' is a mathematically well-behaved class

Source

Wilfrid Hodges (First-Order Logic [2001], 1.6)

Book Ref

'Blackwell Guide to Philosophical Logic', ed/tr. Goble,Lou [Blackwell 2001], p.19

The 8 ideas from 'First-Order Logic'

10282 Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former) [Hodges,W]
10289 Up Löwenheim-Skolem: if infinite models, then arbitrarily large models [Hodges,W]
10288 Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model [Hodges,W]
10287 If a first-order theory entails a sentence, there is a finite subset of the theory which entails it [Hodges,W]
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]
10286 A 'set' is a mathematically well-behaved class [Hodges,W]