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Results tagged with lo.logic
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user 4354
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.
6
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5
answers
2k
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A book explaining power and limitations of Peano Axioms?
Are there books or survey articles explaining the subject to a non-expert? To clarify what I mean, here is a couple of issues that I would like to read about. (I am mainly interested in references but …
- 32.4k
58
votes
9
answers
8k
views
How do they verify a verifier of formalized proofs?
In an unrelated thread Sam Nead intrigued me by mentioning a formalized proof of the Jordan curve theorem. I then found that there are at least two, made on two different systems. This is quite an ach …
- 32.4k
10
votes
Accepted
A decision problem concerning Diophantine inequalities
It is undecidable. If you could solve this, you could also solve Hilbert's 10th problem.
Suppose we have an algorithm solving your problem for all $n$. Given a polynomial $p\in\mathbb[x_1,\dots,x_n]$, …
- 32.4k
6
votes
Is equivalence of functions built from nested exponentiations a decidable problem?
This is a justification of the algorithm suggested in Dan Turetsky's comment.
Every expression in $E$ reduces to an expression in $E'$ which is the minumum language such that $x\in E'$ and $x^{(p_1*\ …
- 32.4k
20
votes
1
answer
907
views
A collection of intervals that can cover any measure zero set
This is a follow-up to this question (in fact, this is what originally motivated me to ask that one.)
Let's say that a sequence $\{s_i\}$ of positive reals covers a set $X\subset\mathbb R$ if there i …
- 32.4k
27
votes
2
answers
2k
views
A set that can be covered by arbitrarily small intervals
Let $X$ be a subset of the real line and $S=\{s_i\}$ an infinite sequence of positive numbers. Let me say that $X$ is $S$-small if there is a collection $\{I_i\}$ of intervals such that the length of …
- 32.4k