Logic List Mailing Archive

The Open Logic Project

It's been a few year since the first announcement, and you may have been 
following the progress of the Open Logic Project. If not, here are some 
updates:

Coverage has grown significantly and now also includes:

   *   Introduction to mathematical proof and induction for novices
   *   Four different proof systems for propositional and first-order logic (axiomatic proofs, tableaux, natural deduction, and sequent calculus)
   *   Second-order logic
   *   Models of arithmetic
   *   Lambda calculus (including equivalence of lambda computable and recursive functions)
   *   Intuitionistic propositional logic
   *   Normal modal logics
   *   Conditional logics (counterfactuals)
   *   Infinity and construction of number systems in naive set theory
   *   Development of set theory in ZFC (ordinal and cardinal arithmetic)
   *   Short biographies of 11 logicians

Thanks to some grant funding I was able to obtain high-quality photos and 
and commission illustrated portraits of several dozen logicians (at 
https://urldefense.proofpoint.com/v2/url?u=https-3A__github.com_OpenLogicProject_photos&d=DwIGaQ&c=slrrB7dE8n7gBJbeO0g-IQ&r=xXZM6ZrkjVxXknjzIxhAvQ&m=0csxuMoWAFoR5Zh_DNC_6Hplg9sg1aleZAvEJwqJdnk&s=99PfY1iwyoOOjEs0it2h4u_GsaHjRTwXzZf97J4yk6M&e= 
and 
https://urldefense.proofpoint.com/v2/url?u=https-3A__github.com_OpenLogicProject_portraits&d=DwIGaQ&c=slrrB7dE8n7gBJbeO0g-IQ&r=xXZM6ZrkjVxXknjzIxhAvQ&m=0csxuMoWAFoR5Zh_DNC_6Hplg9sg1aleZAvEJwqJdnk&s=_Qrq-Gh_l-yfij_Wd-1GWSeLwSezKsSrH6sgryFgtLU&e= 
).

This is all freely available in LaTeX source code and one 900+-page PDF, 
at 
https://urldefense.proofpoint.com/v2/url?u=https-3A__openlogicproject.org_&d=DwIGaQ&c=slrrB7dE8n7gBJbeO0g-IQ&r=xXZM6ZrkjVxXknjzIxhAvQ&m=0csxuMoWAFoR5Zh_DNC_6Hplg9sg1aleZAvEJwqJdnk&s=A0jeH79LuHD0BH9tdpb0CZ_Bjv3Vuqp-ANdH0hfJAgk&e= 
.

As the content is very modular, it is relatively easy to select, reorder, 
and mix and match the content. There are now also four self-contained 
textbooks (of more manageable size) based on the material in the project:

Sets, Logic, Computation covers basic set theory; syntax, semantics, and 
proof theory of first-order logic (natural deduction and sequent 
calculus); completeness, compactness, and Lwenheim-Skolem theorems; 
Turing machines and the halting problem; undecidability of first-order 
logic.

https://urldefense.proofpoint.com/v2/url?u=http-3A__builds.openlogicproject.org_courses_phil379_&d=DwIGaQ&c=slrrB7dE8n7gBJbeO0g-IQ&r=xXZM6ZrkjVxXknjzIxhAvQ&m=0csxuMoWAFoR5Zh_DNC_6Hplg9sg1aleZAvEJwqJdnk&s=l2FFb1vzQUmXLc4Sueq54q2arrzADQxYM1lNLKszXSs&e=

Incompleteness and Computability covers basic recursive function theory, 
arithmetization of syntax (for proof predicates for axiomatic deduction, 
natural deduction, and sequent calculus), representability in Q, first and 
second incompleteness theorems, models of arithmetic, second-order logic, 
lambda calculus.

https://urldefense.proofpoint.com/v2/url?u=http-3A__builds.openlogicproject.org_courses_phil479_&d=DwIGaQ&c=slrrB7dE8n7gBJbeO0g-IQ&r=xXZM6ZrkjVxXknjzIxhAvQ&m=0csxuMoWAFoR5Zh_DNC_6Hplg9sg1aleZAvEJwqJdnk&s=UkVWXqumfAc2JsVdrD8VYHkOP_CMfXWN5_7JI1Ma24g&e=

Boxes and Diamonds covers syntax, semantics, and proof theory of normal 
modal logics (axiomatic deductions and prefixed tableaux), intuitionistic 
propositional logic, and counterfactuals.

https://urldefense.proofpoint.com/v2/url?u=http-3A__builds.openlogicproject.org_courses_boxes-2Dand-2Ddiamonds_&d=DwIGaQ&c=slrrB7dE8n7gBJbeO0g-IQ&r=xXZM6ZrkjVxXknjzIxhAvQ&m=0csxuMoWAFoR5Zh_DNC_6Hplg9sg1aleZAvEJwqJdnk&s=L3OJUaC7p3olP4-cF0khOAEgK0NRv3ZOmH--sHrZuYQ&e=

Set Theory covers development of elementary mathematics in naive set 
theory, the cumulative hierarchy, ordinal and cardinal arithmetic, and the 
axiom of choice.

https://urldefense.proofpoint.com/v2/url?u=http-3A__builds.openlogicproject.org_courses_set-2Dtheory_&d=DwIGaQ&c=slrrB7dE8n7gBJbeO0g-IQ&r=xXZM6ZrkjVxXknjzIxhAvQ&m=0csxuMoWAFoR5Zh_DNC_6Hplg9sg1aleZAvEJwqJdnk&s=U8KcgMBwcGgjEjvwQf-h5qzX0Js-JL5zkgE_Ypykhhs&e=

(Most of the set theory material is brand new, adapted from Tim Button's 
Open Set Theory book).

Richard Zach
--
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