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first-order and higher-order logic, model theory, set theory, proof theory, computability theory, formal languages, definability, interplay of syntax and semantics, constructive logic, intuitionism, philosophical logic, modal logic, completeness, Gödel incompleteness, decidability, undecidability, theories of truth, truth revision, consistency.
1
vote
Complete mathematics
This answer is possibly unhelpful and definitely under-informed, but a good source to look into might be the book Complete Theories by Abraham Robinson. I haven't read it, I just happened to see it a …
12
votes
1
answer
3k
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Up-to-date version of Principia Mathematica?
Background: I found this interesting translation of Godel's On formally undecidable propositions of Principia Mathematica and related systems I that, along with translating it into English, uses more …
1
vote
Borel / Wadge hierarchies on subsets closed under prepending a finite prefix
I am not sure of a specific, good source for you, but it looks like you are interested in sets that are closed under the 'inverse' of the shift map.
The shift $S:A^\omega\to A^\omega$ is $S(x_1,x_2, …
2
votes
Textbook recommendations for undergraduate proof-writing class
The book I used in my 'proofs' class was "Doing Mathematics: An Introduction to Proofs and Problem Solving" by Steven Galovich, here on Amazon.
The class was called "Mathematical Structures", which …