Smith, Peter. 2024. Beginning Mathematical Logic. Logic Matters. https://www.logicmatters.net/resources/pdfs/LogicStudyGuide.pdf.
Smith - 2024 - Beginning Mathematical Logic.pdf.
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Imported: 2024-04-26 10:43 am
model theory which, roughly speaking, explores how formal theories relate to the structures they are about.
relevant logics (where we impose stronger requirements on the relevance of premisses to conclusions for valid arguments)
free logics (logics free of existence assumptions, where we no longer presuppose that e.g. names in an interpreted formal language always actually name something)
plural logics (where we can e.g. cope with plural terms)
This approach will really help to reinforce and deepen understanding as you encounter and re-encounter the same material, coming at it from somewhat different angles, with different emphases.
some authors have the irritating(?) habit of burying quite important results among the exercises, mixed in with routine homework. It is therefore always a good policy to skim through the exercises in a book even if you don’t plan to work on answers to very many of them
A × B is {⟨x, y⟩ | x ∈ A & y ∈ B}
the extension of R is a subset of A × B.
Imported: 2024-04-26 12:22 pm
Two sets are equinumerous if we can match up their members one-to-one
A set is countably infinite if and only if it is equinumerous with the natural numbers.
The Axiom of Choice, in one version, says that, given an infinite family of sets, there is a corresponding choice function–i.e. a function which ‘chooses’ a single member from each set in the family. Bertrand Russell’s toy example: given an infinite collection of pairs of socks, there is a function which chooses one sock from each pair