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Results tagged with lo.logic
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user 6153
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.
8
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Proof theory and primitive roots
I have had this question on my mind for two decades. We know, after Heath-Brown, that one out (say) of 3, 5, 7 is a primitive root mod p for infinitely many primes p. We just don't know which one. (We …
- 44.4k
9
votes
What is the geometry of an undecidable diophantine equation?
You have a typical recursively enumerable set S of integers, and a set X of lattice points cut out by a multivariate polynomial. We are talking about S being the projection (onto one axis) of X. Given …
- 12.6k
0
votes
Did Pogorzelski claim to have a proof of Goldbach's Conjecture?
The "why not" is about the onus of proof. The word "false" does not properly qualify a proof, but a proposition. The procedure by which proofs become accepted as essentially correct is by publication …
- 12.6k
3
votes
Infinite games: are they well defined?
I'm aware of quite a number of theories of "games" in mathematics. A not-overly-naive preliminary is to ask about what these are, and then what they have in common.
I think the earliest is probably …
- 12.6k
4
votes
Stone Spaces, Locales, and Topoi for the (relative) beginner
The texts by Vickers and Johnstone are rather different, and certainly are different in intention. I was struck by a remark made to me by a leading computer scientist, to the effect that Stone Spaces …
- 12.6k
5
votes
Connections between ultrafilters in topology and logic
My feeling, which may be ignorant, is that these intuitions go all the way back to Leibniz. There "point" was in some way ridded of a silly definition like "position but no magnitude", and was replace …
- 12.6k
15
votes
Au revoir, law of excluded middle?
I don't know whether this will be helpful, but here goes. There used to be things called the "Laws of Thought", and they used to be equated (tendentiously) with sort-of axioms for rationality, when "a …
- 12.6k